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Monoidal categories and topological field theory [electronic resource]

Monoidal categories and topological field theory [electronic resource]

자료유형
E-Book(소장)
개인저자
Turaev, Vladimir. Virelizier, Alexis.
서명 / 저자사항
Monoidal categories and topological field theory [electronic resource] / Vladimir Turaev, Alexis Virelizier.
발행사항
Cham :   Springer,   c2017.  
형태사항
1 online resource (xii, 523 p.).
총서사항
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.
일반주기
Title from e-Book title page.  
내용주기
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.
서지주기
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Algebra. Cell aggregation --Mathematics.
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020 ▼a 9783319498331
020 ▼a 9783319498348 (e-book)
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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)

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 중앙도서관/e-Book 컬렉션/ 청구기호 CR 512.62 등록번호 E14016832 도서상태 대출불가(열람가능) 반납예정일 예약 서비스 M

컨텐츠정보

목차

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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