Related papers: Equivariant Elliptic Cohomology and Rigidity
We construct a Thom class in complex equivariant elliptic cohomology extending the equivariant Witten genus. This gives a new proof of the rigidity of the Witten genus, which exhibits a close relationship to recent work on non-equivariant…
Following an outline of Rezk, we give a construction of complex-analytic $G$-equivariant elliptic cohomology for an arbitrary compact Lie group $G$ and we prove some of its fundamental properties. The construction is parametrised over the…
Let M be a spin manifold with a circular action. Given an elliptic curve E, we introduce, as in Grojnowski, elliptic bouquets of germs of holomorphic equivariant cohomology classes on M. Following Bott-Taubes and Rosu, we show that…
We introduce a new cohomology theory for stacks called elliptic Hochschild homology, prove some fundamental properties and compute it in some classes of examples. We then introduce its periodic cyclic version and show that, over the complex…
Kitchloo and Morava give a strikingly simple picture of elliptic cohomology at the Tate curve by studying a completed version of $S^1$-equivariant $K$-theory for spaces. Several authors (cf [ABG],[KM],[L]) have suggested that an equivariant…
Equivariant cohomology is suggested as an alternative algebraic framework for the definition of topological field theories constructed by E. Witten circa 1988. It also enlightens the classical Faddeev Popov gauge fixing procedure.
We construct a cocycle model for complex analytic equivariant elliptic cohomology that refines Grojnowski's theory when the group is connected and Devoto's when the group is finite. We then construct Mathai--Quillen type cocycles for…
We provide a differential cocycle model for elliptic cohomology with complex coefficients and use analytic methods to construct a cocycle representative for the Witten class in this language. Our motivation stems from the conjectural…
We present an Eilenberg-Steenrod-like axiomatic framework for equivariant coarse homology and cohomology theories. We also discuss a general construction of such coarse theories from topological ones and the associated transgression maps. A…
Ginzburg, Kapranov and Vasserot conjectured the existence of equivariant elliptic cohomology theories. In this paper, to give a description of equivariant spectra of the theories, we study an intermediate theory, quasi-elliptic cohomology.…
In this article we study the equivariant elliptic cohomology of complex toric varieties. We prove a partial reconstruction theorem showing that equivariant elliptic cohomology encodes considerable non-trivial information on the equivariant…
For $G$ a finite group, we show that functions on fields for the 2-dimensional supersymmetric sigma model with background $G$-symmetry determine cocycles for complex analytic $G$-equivariant elliptic cohomology. Similar structures in…
Let $k$ be a perfect field of characteristic $p > 0$, $W_n = W_n(k)$. For separated $k$-schemes of finite type, we explain how rigid cohomology with compact supports can be computed as the cohomology of certain de Rham-Witt complexes with…
In 1994, Grojnowski gave a construction of an equivariant elliptic cohomology theory associated to an elliptic curve over the complex numbers. Grojnowski's construction has seen numerous applications in algebraic topology and geometric…
For any finite group G, we show that the 2-local G-equivariant stable homotopy category, indexed on a complete G-universe, has a unique equivariant model in the sense of Quillen model categories. This means that the suspension functor,…
We prove that Schubert and Richardson varieties in flag manifolds are uniquely determined by their equivariant cohomology classes, as well as a stronger result that replaces Schubert varieties with closures of Bialynicki-Birula cells under…
This paper provides an introduction to equivariant cohomology and homology using the approach of Goresky, Kottwitz, and MacPherson. When a group G acts suitably on a variety X, the equivariant cohomology of X can be computed using the…
We develop an equivariant version of Seiberg-Witten-Floer cohomology for finite group actions on rational homology $3$-spheres. Our construction is based on an equivariant version of the Seiberg-Witten-Floer stable homotopy type, as…
In math.AG/0207233, Okounkov and Pandharipande gave an operator formalism for computing the equivariant Gromov-Witten theory of the projective line. This thesis extends their result to orbifold lines. In the effective case the theory is…
We construct {\it Topological Elliptic Genera}, homotopy-theoretic refinements of the elliptic genera for $SU$-manifolds and variants including the Witten-Landweber-Ochanine genus. The codomains are genuinely $G$-equivariant Topological…