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Topics in equivariant cohomology [PDF]
, 2017 The equivariant cohomology of a manifold M acted upon by a compact Lie group G is defined to be the singular cohomology groups of the topological space (M × EG)/G. It is well known that the equivariant cohomology of M is parametrised by the Cartan model of equivariant differential forms.
Keating Hughes, Luke
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Chern–Weil homomorphism in twisted equivariant cohomology [PDF]
Differential Geometry and Its Applications, 2010 We describe the Cartan and Weil models of twisted equivariant cohomology together with the Cartan homomorphism among the two, and we extend the Chern–Weil homomorphism to the twisted equivariant cohomology.
Bernardo Uribe
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NUMERICAL INVARIANTS FOR EQUIVARIANT COHOMOLOGY
The Quarterly Journal of Mathematics, 2013Let \(G\) be a finite or compact Lie group, \(p\) be a prime such that \(G\) has at least one element of order \(p\) and \(X\) be a \(G\)-space. Suppose that the Borel equivariant cohomology ring \(H_G^*(X)=H^*(EG\times_GX, k)\) is finitely generated as a module over \(H^*_G=H^*(BG, k)\).
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EQUIVARIANT COHOMOLOGY AND HOLOMORPHIC INVARIANT
Communications in Contemporary Mathematics, 2008Using equivariant cohomology, we construct a family of holomorphic invariants which include the famous Futaki invariant and its generalization to singular variety as special cases. We are also using this viewpoint to compute the generalized Futaki invariant for complete intersections.
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Equivariant cohomologies and Kähler's geometry
Functional Analysis and Its Applications, 1987An action of a compact Lie group on a symplectic manifold M with symplectic form \(\omega\) is called Hamiltonian, if it preserves the form \(\omega\) and all vector fields which are generated by elements of the Lie algebra are Hamiltonian. Let \(G\times M\to M\) be such an action. Denote by MG the universal fibre space with fibre M.
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Equivariant Cohomology in Topology
1999Let G be a compact Lie group acting on a topological space X. We say that this action is free if, for every p ∈ X,the stabilizer group of p consists solely of the identity. In other words, the action is free if, for every a ∈ G, a ≠ e, the action of a on X has no fixed points.
Victor W. Guillemin +2 more
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Equivariant cohomology, Koszul duality, and the localization theorem
Inventiones Mathematicae, 1997Mark Goresky, Robert Macpherson
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