{"product_id":"quantum-invariants-of-knots-and-vladimir-g-turaev-9783110442663","title":"Quantum Invariants of Knots and 3-Manifolds","description":"\u003cp\u003eDue to the strong appeal and wide use of this monograph, it is now available in its third 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.\u003cbr\u003eThe 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, based on quantum groups and skein modules of tangles in the 3-space.\u003cbr\u003eThis fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. \u003c\/p\u003e \u003cp\u003e\u003cstrong\u003eContents: \u003c\/strong\u003e\u003cbr\u003eInvariants of graphs in Euclidean 3-space and of closed 3-manifolds\u003cbr\u003eFoundations of topological quantum field theory\u003cbr\u003eThree-dimensional topological quantum field theory\u003cbr\u003eTwo-dimensional modular functors\u003cbr\u003e6j-symbols\u003cbr\u003eSimplicial state sums on 3-manifolds\u003cbr\u003eShadows of manifolds and state sums on shadows\u003cbr\u003eConstructions of modular categories\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Vladimir G. Turaev\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3110442663\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783110442663\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e de Gruyter\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 07\/11\/2016\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 608\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 2.50lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.60h x 6.90w x 1.40d\u003c\/p\u003e","brand":"Vladimir G. Turaev","offers":[{"title":"Hardcover","offer_id":44073572860159,"sku":"9783110442663","price":280.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_74a6dbd2-9d90-41f9-a184-bd75af0a9fe5.jpg?v=1685448618","url":"https:\/\/www.whiterainbookhouse.com\/products\/quantum-invariants-of-knots-and-vladimir-g-turaev-9783110442663","provider":"WR Book House","version":"1.0","type":"link"}