國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Monoidal categories and topological ...

SpringerLink (Online service)

Monoidal categories and topological field theory

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Monoidal categories and topological field theoryby Vladimir Turaev, Alexis Virelizier.
作者:	Turaev, Vladimir.
其他作者:	Virelizier, Alexis.
出版者:	Cham :Springer International Publishing :2017.
面頁冊數:	xii, 523 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Categories (Mathematics)
電子資源:	http://dx.doi.org/10.1007/978-3-319-49834-8
ISBN:	9783319498348$q(electronic bk.)

Monoidal categories and topological field theory
Turaev, Vladimir.

Monoidal categories and topological field theory[electronic resource] /by Vladimir Turaev, Alexis Virelizier. - Cham :Springer International Publishing :2017. - xii, 523 p. :ill., digital ;24 cm. - Progress in mathematics,v.3220743-1643 ;. - Progress in mathematics ;v.295..

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.

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 Muger 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.

ISBN: 9783319498348$q(electronic bk.)

Standard No.: 10.1007/978-3-319-49834-8doiSubjects--Topical Terms:

206297
Categories (Mathematics)

LC Class. No.: QA169

Dewey Class. No.: 512.62

Monoidal categories and topological field theory
LDR:02452nmm a2200337 a 4500 001 517844
003 DE-He213
005 20180117133627.0
006 m d
007 cr nn 008maaau
008 180316s2017 gw s 0 eng d
020 $a 9783319498348$q(electronic bk.)
020 $a 9783319498331$q(paper)
024 7 $a 10.1007/978-3-319-49834-8 $2 doi
035 $a 978-3-319-49834-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA169
072 7 $a PBC $2 bicssc
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
082 0 4 $a 512.62 $2 23
090 $a QA169 $b .T929 2017
100 1 $a Turaev, Vladimir. $3 284136
245 1 0 $a Monoidal categories and topological field theory $h [electronic resource] / $c by Vladimir Turaev, Alexis Virelizier.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2017.
300 $a xii, 523 p. : $b ill., digital ; $c 24 cm.
490 1 $a Progress in mathematics, $x 0743-1643 ; $v v.322
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 Muger 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.
650 0 $a Categories (Mathematics) $3 206297
650 0 $a Topological fields. $3 666699
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Category Theory, Homological Algebra. $3 275954
650 2 4 $a Manifolds and Cell Complexes (incl. Diff.Topology) $3 253172
700 1 $a Virelizier, Alexis. $3 787678
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Progress in mathematics ; $v v.295. $3 558269
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-49834-8
950 $a Mathematics and Statistics (Springer-11649)