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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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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 cohomologies and K�hler's geometry
Functional Analysis and Its Applications, 1988An 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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Topics in equivariant cohomology
2017The 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.
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