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arXiv · 2511.00695

Topological insulators and stable isomorphism versus isomorphism of vector bundles

Ralf Meyer
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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.

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Ralf Meyer. 2025-11-01. Topological insulators and stable isomorphism versus isomorphism of vector bundles. https://arxiv.org/abs/2511.00695

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