Open Access
March 2004 Morse theory on Hamiltonian G-spaces and equivariant K-theory
Victor Guillemin, Mikhail Kogan
J. Differential Geom. 66(3): 345-375 (March 2004). DOI: 10.4310/jdg/1098137837


Let G be a torus and M a compact Hamiltonian G-manifold with finite fixed point set M G . If T is a circle subgroup of G with M G =M T , the T-moment map is a Morse function. We will show that the associated Morse stratification of M by unstable manifolds gives one a canonical basis of K G (M). A key ingredient in our proof is the notion of local index I p (a) for aK G (M) and pM G . We will show that corresponding to this stratification there is a basis τ p , pM G , for K G (M) as a module over K G (pt) characterized by the property: I q τ p q p . For M a GKM manifold we give an explicit construction of these τ p 's in terms of the associated GKM graph.


Download Citation

Victor Guillemin. Mikhail Kogan. "Morse theory on Hamiltonian G-spaces and equivariant K-theory." J. Differential Geom. 66 (3) 345 - 375, March 2004.


Published: March 2004
First available in Project Euclid: 18 October 2004

zbMATH: 1071.53048
MathSciNet: MR2106470
Digital Object Identifier: 10.4310/jdg/1098137837

Rights: Copyright © 2004 Lehigh University

Vol.66 • No. 3 • March 2004
Back to Top