Acyclic Chain complexes over the Orbit Category

TL;DR

This paper develops algebraic models for finite G-CW complexes using chain complexes over orbit categories, proves a Dress induction theorem for K-theory, and reinterprets existing results on acyclic complexes.

Contribution

It introduces a p-hypoelementary Dress induction theorem for K-theory over the orbit category, advancing the algebraic understanding of G-CW complexes.

Findings

Proved a Dress induction theorem for K-theory over orbit categories.

Reinterpreted results of Oliver and Kropholler-Wall on acyclic complexes.

Provided algebraic models for finite G-CW complexes with prescribed isotropy.

Abstract

Chain complexes of finitely generated free modules over orbit categories provide natural algebraic models for finite G-CW complexes with prescribed isotropy. We prove a p-hypoelementary Dress induction theorem for K-theory over the orbit category of a finite group, and use it to re-interpret some results of Oliver and Kropholler-Wall on acyclic complexes.