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- catalog abstract "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.".
- catalog contributor b12290083.
- catalog contributor b12290084.
- catalog created "c2001.".
- catalog date "2001".
- catalog date "c2001.".
- catalog dateCopyrighted "c2001.".
- catalog description "Includes bibliographical references (p. [369]-375) and index.".
- catalog description "Introduction and summary of results -- The double category of framed, relative 3-cobordisms -- Tangle-categories and presentation of cobordisms -- Isomorphism between tangle and cobordism categories -- Monoidal categories and monoidal 2-categories -- Coends and construction of Hopf algebras -- Construction of TQFT-Double Functors -- Generalization of modular functor -- A: From quantum field theory of axiomatics -- B: Double categories and double functors -- C: Thick tangles.".
- catalog 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.".
- catalog extent "vi, 379 p. :".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "3540424164 (pbk. : acid-free paper)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1765.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1765".
- catalog issued "2001".
- catalog issued "c2001.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog relation "Also available in an electronic version.".
- catalog subject "510 s 530.14/3 21".
- catalog subject "Algebra.".
- catalog subject "Cell aggregation Mathematics.".
- catalog subject "Mathematical physics.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1765 QC174.45".
- catalog subject "Quantum field theory.".
- catalog subject "Three-manifolds (Topology)".
- catalog tableOfContents "Introduction and summary of results -- The double category of framed, relative 3-cobordisms -- Tangle-categories and presentation of cobordisms -- Isomorphism between tangle and cobordism categories -- Monoidal categories and monoidal 2-categories -- Coends and construction of Hopf algebras -- Construction of TQFT-Double Functors -- Generalization of modular functor -- A: From quantum field theory of axiomatics -- B: Double categories and double functors -- C: Thick tangles.".
- catalog title "Non-semisimple topological quantum field theories for 3-manifolds with corners / Thomas Kerler, Volodymyr V. Lyubashenko.".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".