We present a simple approach to questions of topological orbit equivalence for actions of countable groups on topological and smooth manifolds. For example, for any action of a countable group Γ on a topological manifold where the fixed sets for any element are contained in codimension two submanifolds, every orbit equivalence is equivariant. Even in the presence of larger fixed sets, for actio...

Let G be a finite group acting on vector spaces V and W and consider a smooth G-equivariant mapping f : V → W. This paper addresses the question of the zero set near a zero x of f with isotropy subgroup G. It is known from results of Bierstone and Field on G-transversality theory that the zero set in a neighborhood of x is a stratified set. The purpose of this paper is to partially determine th...

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 ...

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...

We define and study an equivariant E-theory with respect to coactions of Hopf C-algebras; we prove the Baaj-Skandalis duality in this setting. We show that the corresponding equivariant KK-theory of Baaj and Skandalis enjoys an universal property. In the appendix, we look at the different ways of expressing equivariant stability for a functor, and prove an equivariant BrownGreen-Rieffel stabili...

We generalize the constructions of Eisenbud, Fløystad, and Weyman for equivariant minimal free resolutions over the general linear group, and we construct equivariant resolutions over the orthogonal and symplectic groups. We also conjecture and provide some partial results for the existence of an equivariant analogue of Boij–Söderberg decompositions for Betti tables, which were proven to exist ...

We introduce equivariant twisted cohomology of a simplicial set equipped with simplicial action of a discrete group and prove that for suitable twisting function induced from a given equivariant local coefficients, the simplicial version of Bredon-Illman cohomology with local coefficients is isomorphic to equivariant twisted cohomology. The main aim of this paper is to prove a classification th...