ENGLISH

Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners

By Thomas Kerler , Volodymyr V. Lyubashenko (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2001
ISBN
3540424164, 9783540424161
DOI
10.1007/b82618
ISSN
0075-8434
Open Library ID
OL12774880M
Language
english
Format
DJVU
Filesize
3 MB (2823304 bytes)
Series
Lecture Notes in Mathematics 1765
Edition
1
Pages
383\384
Library
Kolxo3
DPI
300
Scanned
yes
Time added
2009-07-20 03:45:11
Commutative Rings and Algebras; Category TheoryHomological Algebra; Manifolds and Cell Complexes

Description

This book presents the (to date) most general approach to combinatorial constructions of topological quantum field theories (TQFTs) in three dimensions. The authors describe extended TQFTs as double functors between two naturally defined double categories: one of topological nature, made of 3-manifolds with corners, the other of algebraic nature, made of linear categories, functors, vector spaces and maps. Atiyah's conventional notion of TQFTs as well as the notion of modular functor from axiomatic conformal field theory are unified in this concept. A large class of such extended modular catergory is constructed, assigning a double functor to every abelian modular category, which does not have to be semisimple.

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