Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology
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Ring structures of mod p equivariant cohomology rings and ring homomorphisms between them
In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...
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Working from first principles, quantization of a class of symmetric Hamiltonian systems whose constraint algebras are not closed is carried out by constructing first the appropriate reduced phase space and then the brst cohomology. The brst operator constructed is equivariant with respect to a subgroup H of the symmetry group G of the system. Using algebraic techniques from equivariant de Rham ...
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We introduce a notion of morphism of CohFT algebras, based on the analogy with A∞ morphisms. We outline the construction of a “quantization” of the classical Kirwan morphism to a morphism of CohFT algebras from the equivariant quantum cohomology of a Gvariety to the quantum cohomology of its geometric invariant theory or symplectic quotient, and an example relating to the orbifold quantum cohom...
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We present a new geometric interpretation of equivariant cohomology in which one replaces a smooth, complex G-variety X by its associated arc space J∞X, with its induced G-action. This not only allows us to obtain geometric classes in equivariant cohomology of arbitrarily high degree, but also provides more flexibility for equivariantly deforming classes and geometrically interpreting multiplic...
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The supersymmetric model developed by Witten [1] to study the equivariant cohomology of a manifold with an isometric circle action is derived from the brst quantization of a simple classical model. The gauge-fixing process is carefully analysed, and demonstrates that different choices of gauge-fixing fermion can lead to different quantum theories.
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