Topological Quantum Field Theories from Subfactors

Vijay Kodiyalam

• Editore: Chapman and Hall/CRC
• Anno: 2019
• ISBN:
  9780429525070
• Edizione: 1
• Argomento: Matematica
• Categoria: Matematica generale

Pure mathematicians have only recently begun a rigorous study of topological quantum field theories (TQFTs). Ocneanu, in particular, showed that subfactors yield TQFTs that complement the Turaev-Viro construction. Until now, however, it has been difficult to find an account of this work that is both detailed and accessible.Topological Quant

Chapter 1

Preliminaries on TQFTs

1.1 Introduction

One of the hopes that motivated the writing up of these notes was that it might be accessible to an audience of which very little specific background preparation was demanded; the hope was that it might be possible to address a person with nothing more than a ‘modicum of mathematical maturity’ and to describe (to such a person) some of the beautiful concepts and ideas that go into this construction (by Ocneanu) of a ‘topological quantum field theory from a finite-depth subfactor’. While the necessary background from the theory of von Neumann algebras is presented (quite rigorously and precisely, and essentially ‘from scratch’) in the third chapter, a prospective reader with no background in topology is offered a somewhat informal discussion, in the Appendix, on some of the basic terms used. After a ve...