Non-semisimple extended topological quantum field theories /

Non-semisimple extended topological quantum field theories /

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Bibliographic Details
Author / Creator:De Renzi, Marco, author
Imprint:Providence, RI : AMS, American Mathematical Society, 2022.
©2022
Description:xi, 161 pages : illustrations ; 26 cm
Language:English
Series:Memoirs of the American Mathematical Society, 0065-9266 ; Number 1364
Memoirs of the American Mathematical Society ; no. 1364.
Subject:
Quantum groups.
Algebraic topology.
Topological fields.
Quantum field theory.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/12735351
Hidden Bibliographic Details
ISBN:1470452693
9781470452698
Notes:"May 22, volume 277, number 1364 (fifth of 6 numbers)."
Includes bibliographical references (pages 159-161).
Table of Contents:
  • Preface
  • Main results
  • Where to find a quantum invariant and a TQFT inside an ETQFT
  • Outline of the construction
  • Structure of the exposition
  • Chapter 1. Relative modular categories
  • 1.1 Pivotal and ribbon linear categories
  • 1.2 Group structures and ribbon graphs
  • 1.3 Group actions and group realizations
  • 1.4 Projective traces and ambidextrous objects
  • 1.5 Relative pre-modular categories
  • 1.6 Main definition
  • 1.7 Relation with semisimple theory
  • Chapter 2. Admissible cobordisms
  • 2.1 Group colourings
  • 2.2 2-Category of decorated cobordisms
  • 2.3 2-Category of admissible cobordisms
  • Chapter 3. Extension of Constantino-Geer-Patureau invariants 3.1 Projective and generic stabilizations
  • 3.2 Constantino-Geer-Patureau invariants
  • 3.3 Universal construction
  • 3.4 Extended universal construction
  • Chapter 4. Combinatorial and topological properties
  • 4.1 Skein equivalence
  • 4.2 Surgery axioms
  • 4.3 Connection, domination, triviality
  • Chapter 5. Graded extensions
  • 5.1 2-Spheres
  • 5.2 3-Discs
  • 5.3 3-Pants
  • 5.4 Graded extended universal construction
  • Chapter 6. Symmetric monoidality
  • 6.1 Graded ETQFT
  • 6.2 Graded TQFT
  • Chapter 7. Characterization of the image
  • 7.1 1-Spheres
  • 7.2 2-Discs
  • 7.3 2-Pants
  • 7.4 2-Cylinders
  • 7.5 Examples of computations
  • Appendix A. Unrolled quantum groups
  • A.1 Even roots of unity
  • A.2 Odd roots of unity
  • Appendix B. Manifolds and cobordisms with corners
  • B.1 Manifolds with corners
  • B.2 Collars
  • B.3 Gluing
  • B.4 Cobordisms with corners
  • Appendix C. Signature defects
  • C.1 Intersection pairings
  • C.2 Lagrangian subspaces
  • C.3 Maslov indices
  • Appendix D. Symmetric monoidal 2-categories
  • D.1 2-Categories
  • D.2 Symmetric monoidal structures
  • Appendix E. Complete linear and graded linear categories
  • E.1 Linear and graded linear categories
  • E.2 Complete linear categories
  • E.3 Complete graded linear categories
  • E.4 Proofs
  • Bibliography

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