The Bott cofiber sequence in deformation K-theory and simultaneous similarity in U(n)

TL;DR

This paper establishes a homotopy cofiber sequence connecting deformation K-theory and deformation representation rings, and applies this to analyze simultaneous similarity of unitary matrices, revealing new topological insights.

Contribution

It introduces a homotopy cofiber sequence linking deformation K-theory with representation rings and applies it to the problem of simultaneous similarity in U(n).

Findings

Homotopy cofiber sequence relating deformation K-theory and representation rings.

Application to simultaneous similarity of unitary matrices.

New topological framework for deformation representation theory.

Abstract

We show that there is a homotopy cofiber sequence of spectra relating Carlsson's deformation K-theory of a group G to its "deformation representation ring," analogous to the Bott periodicity sequence relating connective K-theory to ordinary homology. We then apply this to study simultaneous similarity of unitary matrices.