we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

Let G be a profinite group with a countable basis of neighborhoods of the identity. A cohomology and homology theory for the group G with non-discrete topological coefficients is developed, improving previous expositions of the subject (see [Wi], [R–Z] and [S-W]). Though the category of topological G-modules considered is additive but not abelian, there is a theory of derived functors. All stan...

The structure of equivariant cohomology in non-abelian localization formulas and topological field theories is discussed. Equivariance is formulated in terms of a nilpotent BRST symmetry, and another nilpotent operator which restricts the BRST cohomology onto the equivariant, or basic sector. A superfield formulation is presented and connections to reducible (BFV) quantization of topological Ya...

Canonical quantization of abelian BF -type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological extension of the action and the topological flux quantization conditions, in terms of the Čech cohomology of the underlying spatial manifold, as required for t...

This note will present certain algebraic results obtained by Samuel Eilenberg and the author in a study of the relations between homotopy and homology groups of a topological space. These results yield a homology theory for any abelian group II, in which the low dimensional homology and cohomology groups of n correspond to familiar constructions on II. They depend upon the application of the me...