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Author:

De Renzi, Marco, author

Title:

Non-semisimple extended topological quantum field theories / Marco De Renzi.

Publisher:

AMSAmerican Mathematical Society,

Copyright Date:

2022

Description:

xi, 161 pages : illustrations ; 26 cm.

Subject:

Quantum groups.
Algebraic topology.
Topological fields.
Quantum field theory.

Notes:

"May 2022, volume 277, number 1364 (fifth of 6 numbers)." Includes bibliographical references (pages 159-161).

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.

Series:

Memoirs of the American Mathematical Society, 0065-9266 ; Number 1364

ISBN:

9781470452698
1470452693

OCLC:

(OCoLC)1314258997

Locations:

OVUX522 -- University of Iowa Libraries (Iowa City)