Toeplitz extensions in noncommutative topology and mathematical physics
Francesca Arici, Bram Mesland
TL;DR
This paper reviews Toeplitz extensions in noncommutative topology and their applications in mathematical physics, especially in topological insulators, highlighting their role in operator K-theory and bulk-edge correspondence.
Contribution
It provides a comprehensive overview of Toeplitz extensions and introduces recent applications in solid state physics, connecting operator K-theory with topological insulators.
Findings
Toeplitz algebras are crucial in understanding topological insulators.
The bulk-edge correspondence is analyzed using Toeplitz extensions.
Operator K-theory provides a framework for these physical phenomena.
Abstract
We review the theory of Toeplitz extensions and their role in operator K-theory, including Kasparov's bivariant K-theory. We then discuss the recent applications of Toeplitz algebras in the study of solid state systems, focusing in particular on the bulk-edge correspondence for topological insulators.
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