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Record Nr. |
UNINA9910809716003321 |
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Autore |
Turaev V. G (Vladimir G.), <1954-> |
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Titolo |
Quantum invariants of knots and 3-manifolds / / Vladimir G. Turaev |
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Pubbl/distr/stampa |
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Berlin, : De Gruyter, 2010 |
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ISBN |
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1-282-71603-4 |
9786612716034 |
3-11-022184-5 |
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Edizione |
[2nd rev. ed.] |
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Descrizione fisica |
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1 online resource (604 p.) |
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Collana |
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De Gruyter studies in mathematics, , 0179-0986 ; ; 18 |
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Classificazione |
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Disciplina |
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Soggetti |
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Quantum field theory |
Knot theory |
Three-manifolds (Topology) |
Invariants |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. [571]-588) and index. |
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Nota di contenuto |
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pt. 1. Towards topological field theory -- pt. 2. The shadow world -- pt. 3. Towards modular categories. |
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Sommario/riassunto |
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Due to the strong appeal and wide use of this monograph, it is now available in its second revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, |
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