Topological insulators and stable isomorphism versus isomorphism of vector bundles
K-Theory and Homology
2025-11-04 v1
Abstract
This note gives an overview of the mathematical framework underlying topological insulators, highlighting the connection to K-theory and vector bundles. We see ``real'' and ``quaternionic'' vector bundles arise naturally in the presence of time-reversal symmetry. Our recent results about when stable isomorphism implies isomorphism are summarised, including some ongoing work for G-equivariant K-theory for finite groups. This clarifies when K-theory completely distinguishes topological phases.
Keywords
Cite
@article{arxiv.2511.00695,
title = {Topological insulators and stable isomorphism versus isomorphism of vector bundles},
author = {Ralf Meyer},
journal= {arXiv preprint arXiv:2511.00695},
year = {2025}
}
Comments
This note is based on a conference talk that I gave in a conference in Batumi in September 2025 and contains no new results