2023-03-29 Book

Author: Yosuke Kubota
Language: Japanese


This book summarizes part of the theory of topological phases of matter in condensed matter physics, especially from a mathematical standpoint. In particular, we have tried to give an overview of the field as much as possible, focusing on two main topics: classification of topological phases and mathematical proofs of bulk and boundary correspondences.

Table of contents

  • Introduction
  • Preparations from Functional Analysis
  • Index Theory of Fredholm Operators
  • K-Theory of Operator Algebras
  • Complex Topological Insulators
  • Noncommutative Geometry of Random Operators
  • Coarse Geometry and Topological Phases
  • Topological Insulators and Real K-Theory
  • Spectral Localizers
  • Twisted equivariant K-Theory
  • Topological Crystalline insulator
  • Related Topics
  • Appendix

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