$K$-theory equivariant with respect to an elementary abelian $2$-group

TL;DR

This paper computes the detailed algebraic structure of equivariant K-theory for elementary abelian 2-groups, including coefficients, products, and operations, advancing understanding of equivariant topological invariants.

Contribution

It provides explicit calculations of $RO(A)$-graded coefficients and algebraic operations for $A$-equivariant complex and real K-theory, a novel comprehensive analysis.

Findings

Explicit $RO(A)$-graded coefficients computed

All algebraic operations and structures determined

Enhanced understanding of equivariant K-theory for elementary abelian 2-groups

Abstract

We compute the $RO(A)$-graded coefficients of $A$-equivariant complex and real topological $K$-theory for $A$ a finite elementary abelian $2$-group, together with all products, transfers, restrictions, power operations, and Adams operations.