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Monoidal categories and topological field theory [electronic resource]

Monoidal categories and topological field theory [electronic resource]

Material type
E-Book(소장)
Personal Author
Turaev, Vladimir. Virelizier, Alexis.
Title Statement
Monoidal categories and topological field theory [electronic resource] / Vladimir Turaev, Alexis Virelizier.
Publication, Distribution, etc
Cham :   Springer,   c2017.  
Physical Medium
1 online resource (xii, 523 p.).
Series Statement
Progress in Mathematics,0743-1643 ; 322
ISBN
9783319498331 9783319498348 (e-book)
요약
This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research. Part 1 introduces monoidal categories and several of their classes, including rigid, pivotal, spherical, fusion, braided, and modular categories. It then presents deep theorems of Müger on the center of a pivotal fusion category. These theorems are proved in Part 2 using the theory of Hopf monads. In Part 3 the authors define the notion of a topological quantum field theory (TQFT) and construct a Turaev-Viro-type 3-dimensional state sum TQFT from a spherical fusion category. Lastly, in Part 4 this construction is extended to 3-manifolds with colored ribbon graphs, yielding a so-called graph TQFT (and, consequently, a 3-2-1 extended TQFT). The authors then prove the main result of the monograph: the state sum graph TQFT derived from any spherical fusion category is isomorphic to the Reshetikhin-Turaev surgery graph TQFT derived from the center of that category. The book is of interest to researchers and students studying topological field theory, monoidal categories, Hopf algebras and Hopf monads.
General Note
Title from e-Book title page.  
Content Notes
Introduction -- Part I: Monoidal Categories -- Part 2: Hopf Algebras and Monads -- Part 3: State Sum Topological Field Theory -- Part 4: Graph Topological Field Theory -- Appendices -- Bibliography -- Index.
Bibliography, Etc. Note
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
Algebra. Cell aggregation --Mathematics.
Short cut
URL
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007 cr
008 190806s2017 sz ob 001 0 eng d
020 ▼a 9783319498331
020 ▼a 9783319498348 (e-book)
040 ▼a 211009 ▼c 211009 ▼d 211009
050 4 ▼a QA169
082 0 4 ▼a 512.62 ▼2 23
084 ▼a 512.62 ▼2 DDCK
090 ▼a 512.62
100 1 ▼a Turaev, Vladimir.
245 1 0 ▼a Monoidal categories and topological field theory ▼h [electronic resource] / ▼c Vladimir Turaev, Alexis Virelizier.
260 ▼a Cham : ▼b Springer, ▼c c2017.
300 ▼a 1 online resource (xii, 523 p.).
490 1 ▼a Progress in Mathematics, ▼x 0743-1643 ; ▼v 322
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
505 0 ▼a Introduction -- Part I: Monoidal Categories -- Part 2: Hopf Algebras and Monads -- Part 3: State Sum Topological Field Theory -- Part 4: Graph Topological Field Theory -- Appendices -- Bibliography -- Index.
520 ▼a This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research. Part 1 introduces monoidal categories and several of their classes, including rigid, pivotal, spherical, fusion, braided, and modular categories. It then presents deep theorems of Müger on the center of a pivotal fusion category. These theorems are proved in Part 2 using the theory of Hopf monads. In Part 3 the authors define the notion of a topological quantum field theory (TQFT) and construct a Turaev-Viro-type 3-dimensional state sum TQFT from a spherical fusion category. Lastly, in Part 4 this construction is extended to 3-manifolds with colored ribbon graphs, yielding a so-called graph TQFT (and, consequently, a 3-2-1 extended TQFT). The authors then prove the main result of the monograph: the state sum graph TQFT derived from any spherical fusion category is isomorphic to the Reshetikhin-Turaev surgery graph TQFT derived from the center of that category. The book is of interest to researchers and students studying topological field theory, monoidal categories, Hopf algebras and Hopf monads.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Algebra.
650 0 ▼a Cell aggregation ▼x Mathematics.
700 1 ▼a Virelizier, Alexis.
830 0 ▼a Progress in Mathematics ; ▼v 322.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=https://doi.org/10.1007/978-3-319-49834-8
945 ▼a KLPA
991 ▼a E-Book(소장)

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/e-Book Collection/ Call Number CR 512.62 Accession No. E14016832 Availability Loan can not(reference room) Due Date Make a Reservation Service M

Contents information

Table of Contents

Introduction.- Part I: Monoidal Categories.- Part 2: Hopf Algebras and Monads.- Part 3: State Sum Topological Field Theory.- Part 4: Graph Topological Field Theory.- Appendices.- Bibliography.- Index.


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