Transfers, Centers, and Group Cohomology

Module cohomology group of inverse semigroup algebras

Let $S$ be an inverse semigroup and let $E$ be its subsemigroup of idempotents. In this paper we define the $n$-th module cohomology group of Banach algebras and show that the first module cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ we show that $HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach sp...

Cohomology and Group Representations

Transfers for ramified covering maps in homology and cohomology

Making use of a modified version, due to McCord, of the Dold-Thom construction of ordinary homology, we give a simple topological definition of a transfer for ramified covering maps in homology with arbitrary coefficients. The transfer is induced by a suitable map between topological groups. We also define a new cohomology transfer which is dual to the homology transfer. This duality allows us ...

Orientations and Transfers in Cohomology of Algebraic Varieties

Algebro-geometric cohomology theories are described axiomatically, with a systematic treatment of their orientations. For every oriented theory, transfer mappings are constructed for mappings of smooth varieties that are proper on supports. In some basic cases, transfers are calculated. The presentation is illustrated by motivic cohomology, K-theory, algebraic cobordism, and other examples. The...

Isotropy in Group Cohomology

The analogue of Lagrangians for symplectic forms over finite groups is studied, motivated by the fact that symplectic G-forms with a normal Lagrangian N⊳G are in one-to-one correspondence, up to inflation, with bijective 1-cocycle data on the quotients G/N . This yields a method to construct groups of central type from such quotients, known as Involutive Yang-Baxter groups. Another motivation f...