The Resource Nonsemisimple topological quantum field theories for 3manifolds with corners, Thomas Kerler, Volodymyr V. Lyubashenko
Nonsemisimple topological quantum field theories for 3manifolds with corners, Thomas Kerler, Volodymyr V. Lyubashenko
Resource Information
The item Nonsemisimple topological quantum field theories for 3manifolds with corners, Thomas Kerler, Volodymyr V. Lyubashenko represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Nonsemisimple topological quantum field theories for 3manifolds with corners, Thomas Kerler, Volodymyr V. Lyubashenko represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 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 3manifolds 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
 Language
 eng
 Extent
 1 online resource (vi, 379 pages)
 Contents

 Introduction and summary of results
 The double category of framed, relative 3cobordisms
 Tanglecategories and presentation of cobordisms
 Isomorphism between tangle and cobordism categories
 Monoidal categories and monoidal 2categories
 Coends and construction of Hopf algebras
 Construction of TQFTDouble Functors
 Generalization of modular functor
 A: From quantum field theory of axiomatics
 B: Double categories and double functors
 C: Thick tangles
 Isbn
 9783540446255
 Label
 Nonsemisimple topological quantum field theories for 3manifolds with corners
 Title
 Nonsemisimple topological quantum field theories for 3manifolds with corners
 Statement of responsibility
 Thomas Kerler, Volodymyr V. Lyubashenko
 Language
 eng
 Summary
 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 3manifolds 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
 Cataloging source
 COO
 http://library.link/vocab/creatorDate
 1965
 http://library.link/vocab/creatorName
 Kerler, Thomas
 Dewey number

 510 s
 530.14/3
 Illustrations
 illustrations
 Index
 index present
 Language note
 English
 LC call number

 QA3
 QC174.45
 LC item number
 .L28 no. 1765
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 1959
 http://library.link/vocab/relatedWorkOrContributorName
 Lyubashenko, Volodymyr V.
 Series statement
 Lecture notes in mathematics,
 Series volume
 1765
 http://library.link/vocab/subjectName

 Quantum field theory
 Threemanifolds (Topology)
 Mathematical physics
 Mathematical physics
 Quantum field theory
 Threemanifolds (Topology)
 Label
 Nonsemisimple topological quantum field theories for 3manifolds with corners, Thomas Kerler, Volodymyr V. Lyubashenko
 Bibliography note
 Includes bibliographical references (pages 369375) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction and summary of results  The double category of framed, relative 3cobordisms  Tanglecategories and presentation of cobordisms  Isomorphism between tangle and cobordism categories  Monoidal categories and monoidal 2categories  Coends and construction of Hopf algebras  Construction of TQFTDouble Functors  Generalization of modular functor  A: From quantum field theory of axiomatics  B: Double categories and double functors  C: Thick tangles
 Control code
 50031875
 Dimensions
 unknown
 Extent
 1 online resource (vi, 379 pages)
 Form of item
 online
 Isbn
 9783540446255
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/b82618.
 Other physical details
 illustrations.
 Specific material designation
 remote
 System control number
 (OCoLC)50031875
 Label
 Nonsemisimple topological quantum field theories for 3manifolds with corners, Thomas Kerler, Volodymyr V. Lyubashenko
 Bibliography note
 Includes bibliographical references (pages 369375) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction and summary of results  The double category of framed, relative 3cobordisms  Tanglecategories and presentation of cobordisms  Isomorphism between tangle and cobordism categories  Monoidal categories and monoidal 2categories  Coends and construction of Hopf algebras  Construction of TQFTDouble Functors  Generalization of modular functor  A: From quantum field theory of axiomatics  B: Double categories and double functors  C: Thick tangles
 Control code
 50031875
 Dimensions
 unknown
 Extent
 1 online resource (vi, 379 pages)
 Form of item
 online
 Isbn
 9783540446255
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/b82618.
 Other physical details
 illustrations.
 Specific material designation
 remote
 System control number
 (OCoLC)50031875
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Nonsemisimpletopologicalquantumfieldtheories/xMYcCg9iGI/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Nonsemisimpletopologicalquantumfieldtheories/xMYcCg9iGI/">Nonsemisimple topological quantum field theories for 3manifolds with corners, Thomas Kerler, Volodymyr V. Lyubashenko</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>