This is the first of two interconnected parts: Part I contains the geometric theory of generalized modular forms and their connections with the cooperation algebra for elliptic cohomology, E``∗E``, while Part II is devoted to the more algebraic theory associated with Hecke algebras and stable operations in elliptic cohomology. We investigate the structure of the stable operation algebra E``∗E``...

let $a$ be an abelian topological group and $b$ a trivial topological $a$-module. in this paper we define the second bilinear cohomology with a trivial coefficient. we show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

We rst develop a notion of quadratic form on a locally compact abelian group. Under suitable hypotheses, we construct a probability measure on the set of closed maximal isotropic subspaces of a locally compact quadratic space over Fp. A random subspace chosen with respect to this measure is discrete with probability 1, and the dimension of its intersection with a xed compact open maximal isotro...

Complexes constructed from chains of p-subgroups of a group G provide valuable tools in group theory, for the understanding of p-local structure, in algebraic topology, for the study of classifying spaces and mod-p group cohomology through homology decompositions, and in modular representation theory, where the Lefschetz module associated to the complex of all nonidentity p-subgroups can be reg...

We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients. We then give applications to integration of characteristic classes on symplectic quotients and to indices of transversally elliptic operators. In particular,...

A bstract In this note we review a construction of BPS Hilbert space in an effective supersymmetric quiver theory with 4 supercharges. We argue abstractly that contains elements equivariant generalized cohomology $$ {E}_G^{\ast}\left(-\right) E G ∗ <mml:mfenc...