Excision in equivariant fibred G-theory

TL;DR

This paper extends excision theorems in controlled algebra to equivariant G-theory with fibred control, establishing key features like fibred assembly and fiberwise trivialization for this generalized setting.

Contribution

It introduces a broad generalization of excision theorems in equivariant G-theory incorporating fibred control and bounded actions, along with fundamental characteristic properties.

Findings

Established excision theorems in the new setting

Proved existence of fibred assembly

Demonstrated fiberwise trivialization

Abstract

This paper provides a generalization of excision theorems in controlled algebra in the context of equivariant G-theory with fibred control and families of bounded actions. It also states and proves several characteristic features of this theory such as existence of the fibred assembly and the fibrewise trivialization.