Bounded G-theory with fibred control

TL;DR

This paper develops a new controlled algebra framework combining bounded K-theory and fibred control, with applications in geometric topology, including excision theorems for computational purposes.

Contribution

It introduces a novel controlled algebraic structure that merges bounded K-theory with fibred control, expanding tools for geometric topology.

Findings

Constructed a new controlled algebra with fibred bounded control

Proved controlled excision theorems for computations

Unified bounded K-theory and G-theory approaches

Abstract

We use filtered modules over a Noetherian ring and fibred bounded control on homomorphisms to construct a new kind of controlled algebra with applications in geometric topology. The theory here can be thought of as a "pushout" of the bounded K-theory with fibred control and the controlled G-theory constructed and used by the authors. This paper contains the non-equivariant theory including controlled excision theorems crucial for computations.