Center for diffusion of mathematic journals

 
 
 
 

Les cours du CIRM

Table of contents for this issue | Previous article
Chris Woodward
Moment maps and geometric invariant theory—Corrected version (October 2011)
Les cours du CIRM, 1 no. 1: Hamiltonian Actions: invariants et classification (2010), p. 121-166
Article PDF

Erratum to Volume 1, number 1, pp. 55-98 (2010)

The initial version of these lectures contained a major error. We publish here a corrected version.

Bibliography

[1] R. Abraham and J. Marsden. Foundations of Mechanics. Benjamin/Cummings, Reading, 1978.  MR 515141 |  Zbl 0393.70001
[2] S. Agnihotri and C. Woodward. Eigenvalues of products of unitary matrices and quantum Schubert calculus. Math. Res. Lett., 5(6):817–836, 1998.  MR 1671192 |  Zbl 1004.14013
[3] D. N. Akhiezer. Lie group actions in complex analysis. Aspects of Mathematics, E27. Friedr. Vieweg & Sohn, Braunschweig, 1995.  MR 1334091 |  Zbl 0845.22001
[4] Werner Ballmann, Mikhael Gromov, and Viktor Schroeder. Manifolds of nonpositive curvature, volume 61 of Progress in Mathematics. Birkhäuser Boston Inc., Boston, MA, 1985.  MR 823981 |  Zbl 0591.53001
[5] B. H. Bowditch. A class of incomplete non-positively curved manifolds. Pacific J. Math., 172(1):1–39, 1996.  MR 1379284 |  Zbl 0867.53039
[6] J. Arms, R. Cushman, and M. Gotay. A universal reduction procedure for Hamiltonian group actions. In T. Ratiu, editor, The Geometry of Hamiltonian Systems, volume 22 of Mathematical Sciences Research Institute Publications, Berkeley, 1989, 1991. Springer-Verlag, Berlin-Heidelberg-New York.  MR 1123275 |  Zbl 0742.58016
[7] M. F. Atiyah. Convexity and commuting Hamiltonians. Bull. London Math. Soc., 14:1–15, 1982.  MR 642416 |  Zbl 0482.58013
[8] M. F. Atiyah and R. Bott. A Lefschetz fixed point formula for elliptic complexes. II. Applications. Ann. of Math. (2), 88:451–491, 1968.  MR 232406 |  Zbl 0167.21703
[9] M. F. Atiyah and R. Bott. The moment map and equivariant cohomology. Topology, 23(1):1–28, 1984.  MR 721448 |  Zbl 0521.58025
[10] M. Audin. The Topology of Torus Actions on Symplectic Manifolds, volume 93 of Progress in Mathematics. Birkhäuser, Boston, 1991.  MR 1106194 |  Zbl 0726.57029
[11] C. Beasley and E. Witten. Non-abelian localization for Chern-Simons theory. J. Differential Geom., 70(2):183–323, 2005.  MR 2192257 |  Zbl 1097.58012
[12] P. Belkale. Local systems on $\mathbb{P}^1-S$ for $S$ a finite set. Compositio Math., 129(1):67–86, 2001.  MR 1856023 |  Zbl 1042.14031
[13] P. Belkale and S. Kumar. Eigenvalue problem and a new product in cohomology of flag varieties. Invent. Math., 166(1):185–228, 2006.  MR 2242637 |  Zbl 1106.14037
[14] A. Berenstein and R. Sjamaar. Coadjoint orbits, moment polytopes, and the Hilbert-Mumford criterion. J. Amer. Math. Soc., 13(2):433–466 (electronic), 2000.  MR 1750957 |  Zbl 0979.53092
[15] A. Bialynicki-Birula. Some theorems on actions of algebraic groups. Ann. of Math. (2), 98:480–497, 1973.  MR 366940 |  Zbl 0275.14007
[16] A. M. Bloch and T. S. Ratiu. Convexity and integrability. In Symplectic geometry and mathematical physics (Aix-en-Provence, 1990), volume 99 of Progr. Math., pages 48–79. Birkhäuser Boston, Boston, MA, 1991.  MR 1156534 |  Zbl 0755.53023
[17] R. Bott. Homogeneous vector bundles. Ann. of Math. (2), 66:203–248, 1957.  MR 89473 |  Zbl 0094.35701
[18] M. Brion. Sur l’image de l’application moment. In M.-P. Malliavin, editor, Séminaire d’algèbre Paul Dubreuil et Marie-Paule Malliavin, volume 1296 of Lecture Notes in Mathematics, pages 177–192, Paris, 1986, 1987. Springer-Verlag, Berlin-Heidelberg-New York.  MR 932055 |  Zbl 0667.58012
[19] M. Brion. Groupe de Picard et nombres caractéristiques des variétés sphériques. Duke Math. J., 58(2):397–424, 1989.  MR 1016427 |  Zbl 0701.14052
[20] M. Brion, D. Luna, and Th. Vust. Espaces homogènes sphériques. Invent. Math., 84:617–632, 1986.  MR 837530 |  Zbl 0604.14047
[21] M. Brion and M. Vergne. Lattice points in simple polytopes. J. Amer. Math. Soc., 10:371–392, 1997.  MR 1415319 |  Zbl 0871.52009
[22] L. Bruasse and A. Teleman. Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry. Ann. Inst. Fourier (Grenoble), 55(3):1017–1053, 2005. Cedram |  MR 2149409 |  Zbl 1093.32009
[23] A. Cannas da Silva. Introduction to symplectic and Hamiltonian geometry. Publicações Matemáticas do IMPA. [IMPA Mathematical Publications]. Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2003.  MR 2115646 |  Zbl 1073.53102
[24] Pierre-Emmanuel Caprace and Alexander Lytchak. At infinity of finite-dimensional CAT(0) spaces. Math. Ann., 346(1):1–21, 2010.  MR 2558883 |  Zbl 1184.53038
[25] J. S. Carter, D. E. Flath, and M. Saito. The classical and quantum 6$j$-symbols. Princeton University Press, Princeton, NJ, 1995.  MR 1366832 |  Zbl 0851.17001
[26] X. Chen and S. Sun. Calabi flow, Geodesic rays, and uniqueness of constant scalar curvature Kähler metrics. arXiv:1004.2012.
[27] D. A. Cox. The homogeneous coordinate ring of a toric variety. J. Algebraic Geom., 4(1):17–50, 1995.  MR 1299003 |  Zbl 0846.14032
[28] T. Delzant. Hamiltoniens périodiques et images convexes de l’application moment. Bull. Soc. Math. France, 116:315–339, 1988. Numdam |  MR 984900 |  Zbl 0676.58029
[29] T. Delzant. Classification des actions Hamiltoniennes des groupes de rang $2$. Ann. Global Anal. Geom., 8(1):87–112, 1990.  MR 1075241 |  Zbl 0711.58017
[30] S. K. Donaldson and P. Kronheimer. The geometry of four-manifolds. Oxford Mathematical Monographs. Oxford University Press, New York, 1990.  MR 1079726 |  Zbl 0904.57001
[31] J. J. Duistermaat. Equivariant cohomology and stationary phase. In Symplectic geometry and quantization, (Sanda and Yokohama, 1993), volume 179 of Contemp. Math., pages 45–62, Providence, RI, 1994. Amer. Math. Soc.  MR 1319601 |  Zbl 0852.57029
[32] P. B. Eberlein. Geometry of nonpositively curved manifolds. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1996.  MR 1441541 |  Zbl 0883.53003
[33] D. Feldmüller. Two-orbit varieties with smaller orbit of codimension two. Arch. Math. (Basel), 54(6):582–593, 1990.  MR 1052980 |  Zbl 0668.14031
[34] W. Fulton. Introduction to Toric Varieties, volume 131 of Annals of Mathematics Studies. Princeton University Press, Princeton, 1993.  MR 1234037 |  Zbl 0813.14039
[35] W. Fulton. Eigenvalues, invariant factors, highest weights, and Schubert calculus. Bull. Amer. Math. Soc. (N.S.), 37(3):209–249 (electronic), 2000.  MR 1754641 |  Zbl 0994.15021
[36] A. Grothendieck. Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2). Documents Mathématiques (Paris) [Mathematical Documents (Paris)], 4. Société Mathématique de France, Paris, 2005. Séminaire de Géométrie Algébrique du Bois Marie, 1962, Augmenté d’un exposé de Michèle Raynaud. [With an exposé by Michèle Raynaud], With a preface and edited by Yves Laszlo, Revised reprint of the 1968 French original.  Zbl 0197.47202
[37] V. Guillemin and S. Sternberg. Convexity properties of the moment mapping. Invent. Math., 67:491–513, 1982.  MR 664117 |  Zbl 0503.58017
[38] V. Guillemin and S. Sternberg. Geometric quantization and multiplicities of group representations. Invent. Math., 67:515–538, 1982.  MR 664118 |  Zbl 0503.58018
[39] V. Guillemin and S. Sternberg. Homogeneous quantization and multiplicities of group representations. J. Funct. Anal., 47:344–380, 1982.  MR 665022 |  Zbl 0733.58021
[40] V. Guillemin and S. Sternberg. Geometric Asymptotics, volume 14 of Mathematical Surveys and Monographs. Amer. Math. Soc., Providence, R. I., revised edition, 1990.  MR 516965 |  Zbl 0364.53011
[41] V. Guillemin and S. Sternberg. Symplectic Techniques in Physics. Cambridge Univ. Press, Cambridge, 1990.  MR 1066693 |  Zbl 0734.58005
[42] V. W. Guillemin and S. Sternberg. Supersymmetry and equivariant de Rham theory. Springer-Verlag, Berlin, 1999. With an appendix containing two reprints by Henri Cartan [MR 13,107e; MR 13,107f].  MR 1689252 |  Zbl 0934.55007
[43] V. Guillemin. Kaehler structures on toric varieties. J. Differential Geom., 40(2):285–309, 1994.  MR 1293656 |  Zbl 0813.53042
[44] V. Guillemin and R. Sjamaar. Convexity theorems for varieties invariant under a Borel subgroup. Pure Appl. Math. Q., 2(3, part 1):637–653, 2006.  MR 2252111 |  Zbl 1107.53055
[45] V. Guillemin and S. Sternberg. Multiplicity-free spaces. J. Differential Geom., 19(1):31–56, 1984.  MR 739781 |  Zbl 0548.58017
[46] R. Hartshorne. Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64. With an appendix by P. Deligne. Lecture Notes in Mathematics, No. 20. Springer-Verlag, Berlin, 1966.  MR 222093
[47] J.-C. Hausmann and A. Knutson. The cohomology ring of polygon spaces. Ann. Inst. Fourier (Grenoble), 48(1):281–321, 1998. Cedram |  MR 1614965 |  Zbl 0903.14019
[48] G. J. Heckman. Projections of orbits and asymptotic behavior of multiplicities for compact Lie groups. Invent. Math., 67:333–356, 1982.  MR 665160 |  Zbl 0497.22006
[49] P. Heinzner and F. Loose. Reduction of complex Hamiltonian ${G}$-spaces. Geom. Funct. Anal., 4(3):288–297, 1994.  MR 1274117 |  Zbl 0816.53018
[50] P. Heinzner and A. Huckleberry. Kählerian structures on symplectic reductions. In Complex analysis and algebraic geometry, pages 225–253. de Gruyter, Berlin, 2000.  MR 1760879 |  Zbl 0999.32011
[51] S. Helgason. Differential geometry, Lie groups, and symmetric spaces. Academic Press, New York, 1978.  MR 514561 |  Zbl 0451.53038
[52] Wim H. Hesselink. Uniform instability in reductive groups. J. Reine Angew. Math., 303/304:74–96, 1978.  MR 514673 |  Zbl 0386.20020
[53] Wim H. Hesselink. Desingularizations of varieties of nullforms. Invent. Math., 55(2):141–163, 1979.  MR 553706 |  Zbl 0401.14006
[54] A. Horn. Doubly stochastic matrices and the diagonal of a rotation matrix. Amer. J. Math., 76:620–630, 1954.  MR 63336 |  Zbl 0055.24601
[55] A. Horn. Eigenvalues of sums of Hermitian matrices. Pacific J. Math., 12:225–241, 1962.  MR 140521 |  Zbl 0112.01501
[56] Ignasi Mundet i Riera. A Hilbert–Mumford criterion for polystability in Kaehler geometry, 2008. arXiv.org:0804.1067.  MR 2657676
[57] L. C. Jeffrey and F. C. Kirwan. Localization for nonabelian group actions. Topology, 34:291–327, 1995.  MR 1318878 |  Zbl 0833.55009
[58] V. A. Kaimanovich. Lyapunov exponents, symmetric spaces and a multiplicative ergodic theorem for semisimple Lie groups. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 164(Differentsialnaya Geom. Gruppy Li i Mekh. IX):29–46, 196–197, 1987.  MR 947327 |  Zbl 0696.22012
[59] M. Kapovich, B. Leeb, and J. Millson. Convex functions on symmetric spaces, side lengths of polygons and the stability inequalities for weighted configurations at infinity. J. Differential Geom., 81(2):297–354, 2009.  MR 2472176 |  Zbl 1167.53044
[60] G. Kempf and L. Ness. The length of vectors in representation spaces. In K. Lonsted, editor, Algebraic Geometry, volume 732 of Lecture Notes in Mathematics, pages 233–244, Copenhagen, 1978, 1979. Springer-Verlag, Berlin-Heidelberg-New York.  MR 555701 |  Zbl 0407.22012
[61] F. C. Kirwan. Cohomology of Quotients in Symplectic and Algebraic Geometry, volume 31 of Mathematical Notes. Princeton Univ. Press, Princeton, 1984.  MR 766741 |  Zbl 0553.14020
[62] F. C. Kirwan. Convexity properties of the moment mapping, III. Invent. Math., 77:547–552, 1984.  MR 759257 |  Zbl 0561.58016
[63] A. A. Klyachko. Equivariant vector bundles on toric varieties and some problems of linear algebra. In Topics in algebra, Part 2 (Warsaw, 1988), pages 345–355. PWN, Warsaw, 1990.  MR 1171283 |  Zbl 0761.14017
[64] F. Knop. Automorphisms of multiplicity free Hamiltonian manifolds. arXiv:1002.4256.  MR 2748401
[65] F. Knop. The Luna-Vust theory of spherical embeddings. In Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989), pages 225–249, Madras, 1991. Manoj Prakashan.  MR 1131314 |  Zbl 0812.20023
[66] A. Knutson and T. Tao. The honeycomb model of ${\rm {g}{l}}_n({\bf {c}})$ tensor products. I. Proof of the saturation conjecture. J. Amer. Math. Soc., 12(4):1055–1090, 1999.  MR 1671451 |  Zbl 0944.05097
[67] A. Knutson and T. Tao. Honeycombs and sums of Hermitian matrices. Notices Amer. Math. Soc., 48(2):175–186, 2001.  MR 1811121 |  Zbl 1047.15006
[68] A. Knutson, T. Tao, and C. Woodward. The honeycomb model of ${\rm GL}_n(\mathbb{C})$ tensor products. II. Puzzles determine facets of the Littlewood-Richardson cone. J. Amer. Math. Soc., 17(1):19–48 (electronic), 2004.  MR 2015329 |  Zbl 1043.05111
[69] A. Knutson, T. Tao, and C. Woodward. A positive proof of the Littlewood-Richardson rule using the octahedron recurrence. Electron. J. Combin., 11(1):Research Paper 61, 18 pp. (electronic), 2004.  MR 2097327 |  Zbl 1053.05119
[70] B. Kostant. Quantization and unitary representations. In C. T. Taam, editor, Lectures in Modern Analysis and Applications III, volume 170 of Lecture Notes in Mathematics, pages 87–208, Washington, D.C., 1970. Springer-Verlag, Berlin-Heidelberg-New York.  MR 294568 |  Zbl 0223.53028
[71] Bertram Kostant. On convexity, the Weyl group and the Iwasawa decomposition. Ann. Sci. École Norm. Sup. (4), 6:413–455 (1974), 1973. Numdam |  MR 364552 |  Zbl 0293.22019
[72] E. Lerman. Symplectic cuts. Math. Res. Letters, 2:247–258, 1995.  MR 1338784 |  Zbl 0835.53034
[73] E. Lerman, E. Meinrenken, S. Tolman, and C. Woodward. Non-abelian convexity by symplectic cuts. Topology, 37:245–259, 1998.  MR 1489203 |  Zbl 0913.58023
[74] E. Lerman. Gradient flow of the norm squared of a moment map. Enseign. Math. (2), 51(1-2):117–127, 2005.  MR 2154623 |  Zbl 1103.53051
[75] I. V. Losev. Proof of the Knop conjecture. Ann. Inst. Fourier (Grenoble), 59(3):1105–1134, 2009. Cedram |  MR 2543664 |  Zbl 1191.14075
[76] D. Luna. Slices étales. Sur les groupes algébriques, Mém. Soc. Math. France, 33:81–105, 1973. Numdam |  MR 342523 |  Zbl 0286.14014
[77] D. Luna and Th. Vust. Plongements d’espaces homogènes. Comment. Math. Helv., 58(2):186–245, 1983.  MR 705534 |  Zbl 0545.14010
[78] I. G. Macdonald. Symmetric functions and Hall polynomials. Oxford University Press, New York, 1995. With contributions by A. Zelevinsky.  MR 1354144 |  Zbl 0824.05059
[79] J. Marsden and A. Weinstein. Reduction of symplectic manifolds with symmetry. Rep. Math. Phys., 5:121–130, 1974.  MR 402819 |  Zbl 0327.58005
[80] E. Meinrenken. Symplectic surgery and the Spin$^{\rm c}$-Dirac operator. Adv. in Math., 134:240–277, 1998.  MR 1617809 |  Zbl 0929.53045
[81] K. Meyer. Symmetries and integrals in mathematics. In M. M. Peixoto, editor, Dynamical Systems, Univ. of Bahia, 1971, 1973. Academic Press, New York.  MR 331427
[82] D. Mumford, J. Fogarty, and F. Kirwan. Geometric Invariant Theory, volume 34 of Ergebnisse der Mathematik und ihrer Grenzgebiete, 2. Folge. Springer-Verlag, Berlin-Heidelberg-New York, third edition, 1994.  MR 1304906 |  Zbl 0147.39304
[83] M. S. Narasimhan and C. S. Seshadri. Stable and unitary vector bundles on a compact Riemann surface. Ann. of Math. (2), 82:540–567, 1965.  MR 184252 |  Zbl 0171.04803
[84] L. Ness. A stratification of the null cone via the moment map. Amer. J. Math., 106(6):1281–1329, 1984. with an appendix by D. Mumford.  MR 765581 |  Zbl 0604.14006
[85] P. E. Newstead. Introduction to moduli problems and orbit spaces, volume 51 of Tata Institute of Fundamental Research Lectures on Mathematics and Physics. Tata Institute of Fundamental Research, Bombay, 1978.  MR 546290 |  Zbl 0411.14003
[86] P. E. Newstead. Geometric invariant theory. In Moduli spaces and vector bundles, volume 359 of London Math. Soc. Lecture Note Ser., pages 99–127. Cambridge Univ. Press, Cambridge, 2009.  MR 2537067 |  Zbl 1187.14054
[87] T. Oda. Convex bodies and algebraic geometry, volume 15 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]. Springer-Verlag, Berlin, 1988. An introduction to the theory of toric varieties, Translated from the Japanese.  MR 922894 |  Zbl 0628.52002
[88] P.-E. Paradan. The moment map and equivariant cohomology with generalized coefficients. Topology, 39(2):401–444, 2000.  MR 1722000 |  Zbl 0941.37050
[89] P.-E. Paradan. Localization of the Riemann-Roch character. J. Funct. Anal., 187(2):442–509, 2001.  MR 1875155 |  Zbl 1001.53062
[90] S. Ramanan and A. Ramanathan. Some remarks on the instability flag. Tohoku Math. J. (2), 36(2):269–291, 1984.  MR 742599 |  Zbl 0567.14027
[91] N. Ressayre. Geometric invariant theory and generalized eigenvalue problem. arXiv:0704.2127.  MR 2609246 |  Zbl 1197.14051
[92] J. Roberts. Asymptotics and 6j-symbols. Geom. Topol. Monogr., 4:245–261, 2002. math.QA/0201177.  MR 2002614 |  Zbl 1012.22037
[93] A. H. W. Schmitt. Geometric invariant theory and decorated principal bundles. Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Zürich, 2008.  MR 2437660 |  Zbl 1159.14001
[94] I. Schur. über eine klasse von mittelbindungen mit anwendungen auf der determinanten theorie. S. B. Berlin Math. Ges., 22:9–20, 1923.  JFM 49.0054.01
[95] J. -P. Serre. Représentations linéaires et espaces homogènes kählériens des groupes de Lie compacts (d’après Armand Borel et André Weil). In Séminaire Bourbaki, Vol. 2, pages Exp. No. 100, 447–454. Soc. Math. France, Paris, 1995. Numdam |  MR 1609256 |  Zbl 0121.16203
[96] C. S. Seshadri. Fibrés vectoriels sur les courbes algébriques, volume 96 of Astérisque. Société Mathématique de France, Paris, 1982. Notes written by J.-M. Drezet from a course at the École Normale Supérieure, June 1980.  MR 699278 |  Zbl 0517.14008
[97] S. S. Shatz. The decomposition and specialization of algebraic families of vector bundles. Compositio Math., 35(2):163–187, 1977. Numdam |  MR 498573 |  Zbl 0371.14010
[98] G. C. Shephard. An elementary proof of Gram’s theorem for convex polytopes. Canad. J. Math., 19:1214–1217, 1967.  MR 225228 |  Zbl 0157.52504
[99] R. Sjamaar. Holomorphic slices, symplectic reduction and multiplicities of representations. Ann. of Math. (2), 141:87–129, 1995.  MR 1314032 |  Zbl 0827.32030
[100] R. Sjamaar and E. Lerman. Stratified symplectic spaces and reduction. Ann. of Math. (2), 134:375–422, 1991.  MR 1127479 |  Zbl 0759.58019
[101] P. Slodowy. Die Theorie der optimalen Einparameteruntergruppen für instabile Vektoren. In Algebraische Transformationsgruppen und Invariantentheorie, volume 13 of DMV Sem., pages 115–131. Birkhäuser, Basel, 1989.  MR 1044588 |  Zbl 0753.14006
[102] G. Székelyhidi. Extremal metrics and K-stability (PhD thesis). arxiv:math/0611002.  MR 2303522
[103] A. Teleman. Symplectic stability, analytic stability in non-algebraic complex geometry. Internat. J. Math., 15(2):183–209, 2004.  MR 2055369 |  Zbl 1089.53058
[104] C. Teleman. The quantization conjecture revisited. Ann. of Math. (2), 152(1):1–43, 2000.  MR 1792291 |  Zbl 0980.53102
[105] R. P. Thomas. Notes on GIT and symplectic reduction for bundles and varieties. In Surveys in differential geometry. Vol. X, volume 10 of Surv. Differ. Geom., pages 221–273. Int. Press, Somerville, MA, 2006.  MR 2408226 |  Zbl 1132.14043
[106] G. Tian. On a set of polarized Kähler metrics on algebraic manifolds. J. Differential Geom., 32(1):99–130, 1990.  MR 1064867 |  Zbl 0706.53036
[107] Katrin Wehrheim and Chris T. Woodward. Functoriality for Lagrangian correspondences in Floer theory. Quantum Topol., 1:129–170, 2010.  MR 2657646 |  Zbl 1206.53088
[108] A. Weinstein. The symplectic “category”. In Differential geometric methods in mathematical physics (Clausthal, 1980), volume 905 of Lecture Notes in Math., pages 45–51. Springer, Berlin, 1982.  MR 657441 |  Zbl 0486.58017
[109] E. Witten. Two-dimensional gauge theories revisited. J. Geom. Phys., 9:303–368, 1992.  MR 1185834 |  Zbl 0768.53042
[110] E. Witten. Holomorphic Morse inequalities. In Algebraic and differential topology—global differential geometry, volume 70 of Teubner-Texte Math., pages 318–333. Teubner, Leipzig, 1984.  MR 792703 |  Zbl 0588.32009
[111] C. Woodward. The classification of transversal multiplicity-free group actions. Ann. Global Anal. Geom., 14:3–42, 1996.  MR 1375064 |  Zbl 0877.58022
[112] C. Woodward. Multiplicity-free Hamiltonian actions need not be Kähler. Invent. Math., 131(2):311–319, 1998.  MR 1608579 |  Zbl 0902.58014
[113] C. T. Woodward. Localization via the norm-square of the moment map and the two-dimensional Yang-Mills integral. J. Symp. Geom., 3(1):17–55, 2006.  MR 2198772 |  Zbl 1103.53052
[114] S. Wu. Equivariant holomorphic Morse inequalities. II. Torus and non-abelian group actions. J. Differential Geom., 51(3):401–429, 1999.  MR 1726735 |  Zbl 1024.58007
Copyright Cellule MathDoc 2019 | Credit | Site Map