On cohomology of invariant submanifolds of Hamiltonian actions

2003/09/17 by Yildiray Ozan, Ozan, Yildiray
Mathematics · #53D05 #53D12 (Primary) #57R91 (Secondary) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:53D05 #msc:53D12 #msc:57R91

paper · pdf · doi:10.48550/arxiv.math/0309288

6 pages, corrected typos

arxiv created 2005/03/15 · arxiv updated 2009/12/01

Abstract

In this note we prove the following theorem: Let G be a compact Lie group acting on a compact symplectic manifold M in a Hamiltonian fashion. If L is an l-dimensional closed invariant submanifold of M, on which the G-action is locally free then the fundamental class [L] is trivial in H_l(M,\mathbb Q). We also prove similar results for lower homology groups of L, in case the group G is a finite product of copies of S¹ and SU(2). The key ingredients of the proofs are Kirwan's theorem that Hamiltonian spaces are equivariantly formal and symplectic reduction.

Related

• Hamiltonian Actions on Homogeneous Bounded Domains
• Background Cohomology and Symplectic Reduction
• The equivariant cohomology of Hamiltonian G-spaces From Residual S¹ Actions
• Hamiltonian actions and Lagrangian homogeneous submanifolds
• Equivariant symplectic Hodge theory and the d_Gδ-lemma