Don’t miss it—Apress Access is only $99 for the holiday season! Subscribe now >>

Progress in Mathematics

Monoidal Categories and Topological Field Theory

Authors: Turaev, Vladimir, Virelizier, Alexis

  • Offers a detailed exposition accessible to students
  • Provides numerous figures
  • Winner of the 2016 Ferran Sunyer i Balaguer Prize
see more benefits

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-3-319-49834-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA
  • ISBN 978-3-319-49833-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.99
price for USA
  • ISBN 978-3-319-84250-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research.

Part 1 introduces monoidal categories and several of their classes, including rigid, pivotal, spherical, fusion, braided, and modular categories. It then presents deep theorems of Müger on the center of a pivotal fusion category. These theorems are proved in Part 2 using the theory of Hopf monads. In Part 3 the authors define the notion of a topological quantum field theory (TQFT) and construct a Turaev-Viro-type 3-dimensional state sum TQFT from a spherical fusion category. Lastly, in Part 4 this construction is extended to 3-manifolds with colored ribbon graphs, yielding a so-called graph TQFT (and, consequently, a 3-2-1 extended TQFT). The authors then prove the main result of the monograph: the state sum graph TQFT derived from any spherical fusion category is isomorphic to the Reshetikhin-Turaev surgery graph TQFT derived from the center of that category.

The book is of interest to researchers and students studying topological field theory, monoidal categories, Hopf algebras and Hopf monads.

 

Table of contents (17 chapters)

  • Monoidal categories and functors

    Turaev, Vladimir (et al.)

    Pages 3-30

  • The graphical calculus

    Turaev, Vladimir (et al.)

    Pages 31-51

  • Braided categories

    Turaev, Vladimir (et al.)

    Pages 53-63

  • Fusion categories

    Turaev, Vladimir (et al.)

    Pages 65-87

  • The center of a monoidal category

    Turaev, Vladimir (et al.)

    Pages 89-96

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-3-319-49834-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA
  • ISBN 978-3-319-49833-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.99
price for USA
  • ISBN 978-3-319-84250-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Bibliographic Information

Bibliographic Information
Book Title
Monoidal Categories and Topological Field Theory
Authors
Series Title
Progress in Mathematics
Series Volume
322
Copyright
2017
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-49834-8
DOI
10.1007/978-3-319-49834-8
Hardcover ISBN
978-3-319-49833-1
Softcover ISBN
978-3-319-84250-9
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XII, 523
Topics