Non-semisimple extended topological quantum field theories

Non-semisimple extended topological quantum field theories

Saved in:
Bibliographic Details
Main Author : De Renzi Marco (Auteur)
Format : Book
Language : anglais
Title statement : Non-semisimple extended topological quantum field theories / Marco De Renzi
Published : Providence (R.I.) : American Mathematical Society , C 2022
Physical Description : 1 vol. (XI-161 p.)
Series : Memoirs of the American Mathematical Society ; 1364
Subjects :
Groupes quantiques
Topologie algébrique
Champs, Théorie quantique relativiste des
  • 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