Proceedings of the American Mathematical Society

Author(s): Hui Li
Journal: Proc. Amer. Math. Soc. 131 (2003), 3579-3582.
MSC (2000): Primary 53D05, 53D20; Secondary 55Q05, 57R19
Posted: February 14, 2003
Retrieve article in: PDF

Abstract: Let $(M, \omega)$ be a connected, compact symplectic manifold equipped with a Hamiltonian

action. We prove that, as fundamental groups of topological spaces, $\pi_1(M)=\pi_1(\hbox{minimum})=\pi_1(\hbox{maximum})=\pi_1(M_{red})$ , where $M_{red}$ is the symplectic quotient at any value in the image of the moment map $\phi$ .

1.: M. Atiyah, Convexity and commuting Hamiltonians, Bull. Lond. Math. Soc. 14 (1982), 1-15. MR 83e:53037
2.: M. Audin, The Topology of Torus Actions on Symplectic Manifolds, Progress in Mathematics 93, Birkhäuser, Boston (1991). MR 92m:57046
3.: R. Bott, Non-degenerate critical manifolds, Ann of Math., 60 (1954), 248-261. MR 16:276f
4.: M. Brion and C. Procesi, Action d'un tore dans une vari $\acute{e}$ t $\acute{e}$ projective, Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, Progress in Mathematics 92, Birkhäuser, Boston (1990). MR 92m:14061
5.: W. Chen, A Homotopy Theory of Orbispaces, math. AT/0102020.
6.: V. Guillemin and S. Sternberg, Birational equivalence in the symplectic category, Invent. Math. 97, 485-522 (1989). MR 90f:58060
7.: J. Milnor, Morse theory, Princeton University Press, 1963. MR 29:634
8.: C. M. Marle, Mod $\acute{e}$ le d'action hamiltonienne d'un groupe de Lie sur une vari $\acute{e}$ t $\acute{e}$ symplectique, Rendiconti del Seminario Matematico 43 (1985), 227-251, Univ. Politechnico, Torino. MR 88a:58075
9.: D. McDuff, Examples of simply-connected symplectic non-K $\Ddot{a}$ hlerian manifolds, Differential Geometry 20 (1984), 267-277. MR 86c:57036
10.: R. Sjamaar and E. Lerman, Stratified symplectic spaces and reduction, Ann. of Math. (2) 134 (1991), no. 2, 375-422. MR 92g:58036
11.: Y. Takeuchi and M. Yokoyama, The geometric realizations of the decompositions of 3-orbifold fundamental groups, Topology Appl. 95 (1999) no. 2, 129-153. MR 2000g:57028

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53D05, 53D20, 55Q05, 57R19

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS