On the K-theoretic classification of dynamically stable systems

TL;DR

This paper develops a specialized topological K-theory framework to classify topological phases of dynamically stable systems modeled by gapped η-self-adjoint operators on Krein spaces with indefinite metrics.

Contribution

It introduces a new K-theoretic approach tailored for classifying topological phases in systems with indefinite metrics and self-adjoint operators.

Findings

Constructed a topological K-theory for η-self-adjoint operators

Classified topological phases of systems with indefinite metrics

Provided mathematical tools for analyzing stability in such systems

Abstract

This paper deals with the construction of a suitable topological $K$-theory capable of classifying topological phases of dynamically stable systems described by gapped $\eta$-self-adjoint operators on a Krein space with indefinite metric $\eta$.