Symmetric cohomology of groups as a Mackey functor

TL;DR

This paper develops the theory of symmetric cohomology of groups, establishing that it forms a Mackey functor with well-defined restriction, conjugation, and transfer maps, and explores new properties using normalized cochains.

Contribution

It introduces a Mackey functor structure for symmetric cohomology of groups and presents new properties derived from normalized cochains.

Findings

Symmetric cohomology admits restriction, conjugation, and transfer maps.

These maps form a Mackey functor under restriction.

New properties of symmetric cohomology are established using normalized cochains.

Abstract

Symmetric cohomology of groups, defined by M. Staic in [2], is similar to the way one defines the cyclic cohomology for algebras. We show that there is a well-defined restriction, conjugation and transfer map in symmetric cohomology, which form a Mackey functor under a restriction. Some new properties for the symmetric cohomology group using normalized cochains are also given.