A configuration space for equivariant connective K-homology

TL;DR

This paper constructs an equivariant configuration space model for connective K-homology of finite groups, providing explicit homology descriptions and an induction structure, advancing the understanding of equivariant algebraic topology.

Contribution

It introduces a new configuration space model for equivariant connective K-homology and details its homology and induction structure, extending Segal's ideas.

Findings

Explicit homology with complex coefficients for fixed points as a Hopf algebra

Construction of an equivariant configuration space model for connective K-homology

Establishment of an induction structure for the theory

Abstract

Following ideas of Graeme Segal, we construct an equivariant con- figuration space that is a model of equivariant connective K-homology spec- trum for finite groups, as a consequence we obtain an induction structure for equivariant connective K-homology. We describe explicitly the homology with complex coefficients for the fixed points of this configuration space as a Hopf algebra.