Volume 9, issue 1 (2005)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
Homotopy properties of Hamiltonian group actions

Jarek Kędra and Dusa McDuff

Geometry & Topology 9 (2005) 121–162

arXiv: math.SG/0404539


Consider a Hamiltonian action of a compact Lie group G on a compact symplectic manifold (M,ω) and let G be a subgroup of the diffeomorphism group DiffM. We develop techniques to decide when the maps on rational homotopy and rational homology induced by the classifying map BG BG are injective. For example, we extend Reznikov’s result for complex projective space n to show that both in this case and the case of generalized flag manifolds the natural map H(BSU(n + 1)) H(BG) is injective, where G denotes the group of all diffeomorphisms that act trivially on cohomology. We also show that if λ is a Hamiltonian circle action that contracts in G := Ham(M,ω) then there is an associated nonzero element in π3(G) that deloops to a nonzero element of H4(BG). This result (as well as many others) extends to c-symplectic manifolds (M,a), ie, 2n–manifolds with a class a H2(M) such that an0. The proofs are based on calculations of certain characteristic classes and elementary homotopy theory.

symplectomorphism, Hamiltonian action, symplectic characteristic class, fiber integration
Mathematical Subject Classification 2000
Primary: 53C15
Secondary: 53D05, 55R40, 57R17
Forward citations
Received: 30 April 2004
Revised: 22 December 2004
Accepted: 27 December 2004
Published: 28 December 2004
Proposed: Ralph Cohen
Seconded: Leonid Polterovich, Frances Kirwan
Jarek Kędra
Institute of Mathematics US
Wielkopolska 15
70-451 Szczecin
Dusa McDuff
Department of Mathematics
Stony Brook University
Stony Brook
New York 11794-3651