Condensed Matter Physics and Topology - From the Viewpoint of Noncommutative Geometry

Description

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