Geometry, Mechanics, and Dynamics
DOI: 10.1007/0-387-21791-6_12
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Combinatorial Formulas for Products of Thom Classes

Abstract: Abstract. Let G be a torus of dimension n > 1 and M a compact Hamiltonian G-manifold with M G finite. A circle, For manifolds of GKM type we obtain a combinatorial description of these τ + p 's and, from this description, a combinatorial formula for c r pq . Products of Thom classesLet M 2d be a compact Hamiltonian S 1 -manifold with moment map, φ : M → R. If M S 1 is finite, φ is a Morse function, and its critical points, p ∈ M S 1 , are all of even index. This has important consequences for the topology of M… Show more

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Cited by 17 publications
(14 citation statements)
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“…There are several attempts to find bases of the equivariant cohomology of a complex variety with an action of T . Guillemin and Zara [22,23] introduced 'equivariant Thom classes' which can be considered as the equivariant Poincaré duals of the closures of the minus cells when the closures are smooth. Goldin and Tolman [18] considered a similar problem for Hamiltonian pS 1 q k -manifolds.…”
Section: 2mentioning
confidence: 99%
“…There are several attempts to find bases of the equivariant cohomology of a complex variety with an action of T . Guillemin and Zara [22,23] introduced 'equivariant Thom classes' which can be considered as the equivariant Poincaré duals of the closures of the minus cells when the closures are smooth. Goldin and Tolman [18] considered a similar problem for Hamiltonian pS 1 q k -manifolds.…”
Section: 2mentioning
confidence: 99%
“…(Here τ p (q) denotes the restriction of τ p to the fixed point q ∈ M T .) Canonical classes were introduced by Goldin and Tolman [GT09], inspired by previous work of Guillemin and Zara [GZ02] (see also [ST]). They do not always exist, however when they exist they are uniquely characterized by (M, ω, ϕ) and satisfy property (ii) of Lemma 5.1.…”
Section: A Characterization Of Cohomological Assignmentsmentioning
confidence: 99%
“…4 There are many variants on the definition of GKM actions (see e.g. [20][21][22][23]). In particular, in less restrictive versions,…”
Section: Gkm Spacesmentioning
confidence: 99%