Equivariant Localization: BV-geometry and Supersymmetric Dynamics

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 ...

Stability Criteria and Classification of Singularities for Equivariant Lagrangian Subwianifolds

One of the useful methods of mathematical physics is the one arising from symplectic geometry and associating the singularities of Lagrangian submanifolds with the optical caustics, phase transitions, bifurcation patterns, obstacle geometry etc. In this paper we derive the stability criteria for singularities of rquivariant Lagrangian submanifolds with a compact Lie group action determined by a...

Equivariant Cohomology in Algebraic Geometry Lecture Five: Projective Space; Localization Ii

ar X iv : m at h / 03 09 06 8 v 1 [ m at h . D G ] 4 S ep 2 00 3 GENERALIZING THE LOCALIZATION FORMULA IN EQUIVARIANT COHOMOLOGY

We give two generalizations of the Atiyah-Bott-Berline-Vergne lo-calization theorem for the equivariant cohomology of a torus action: 1) replacing the torus action by a compact connected Lie group action, 2) replacing the manifold having a torus action by an equivariant map. This provides a systematic method for calculating the Gysin homomorphism in ordinary co-homology of an equivariant map. A...

Equivariant Localization of Path Integrals

We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing the relations with integrable and topological quantum field theories. Beginning with a detailed review of the relevant mathematical background – equivariant ...