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Monoidal Categories and Topological Field Theory (Hardcover, 1st ed. 2017): Vladimir Turaev, Alexis Virelizier Monoidal Categories and Topological Field Theory (Hardcover, 1st ed. 2017)
Vladimir Turaev, Alexis Virelizier
R5,687 Discovery Miles 56 870 Ships in 12 - 17 working days

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.

Monoidal Categories and Topological Field Theory (Paperback, Softcover reprint of the original 1st ed. 2017): Vladimir Turaev,... Monoidal Categories and Topological Field Theory (Paperback, Softcover reprint of the original 1st ed. 2017)
Vladimir Turaev, Alexis Virelizier
R5,018 Discovery Miles 50 180 Ships in 10 - 15 working days

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.

Torsions of 3-dimensional Manifolds (Paperback, 2002 ed.): Vladimir Turaev Torsions of 3-dimensional Manifolds (Paperback, 2002 ed.)
Vladimir Turaev
R1,445 Discovery Miles 14 450 Ships in 10 - 15 working days

From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." -Zentralblatt Math

"This monograph contains a wealth of information many topologists will find very handy. ...Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." -Mathematical Reviews

Braid Groups (Paperback, Softcover reprint of hardcover 1st ed. 2008): Christian Kassel Braid Groups (Paperback, Softcover reprint of hardcover 1st ed. 2008)
Christian Kassel; Designed by O. Dodane; Vladimir Turaev
R1,847 Discovery Miles 18 470 Ships in 10 - 15 working days

In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices.

Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines.

Torsions of 3-dimensional Manifolds (Hardcover, 2002 ed.): Vladimir Turaev Torsions of 3-dimensional Manifolds (Hardcover, 2002 ed.)
Vladimir Turaev
R1,478 Discovery Miles 14 780 Ships in 10 - 15 working days

From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." -Zentralblatt Math

"This monograph contains a wealth of information many topologists will find very handy. ...Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." -Mathematical Reviews

Braid Groups (Hardcover, 2008 ed.): Christian Kassel Braid Groups (Hardcover, 2008 ed.)
Christian Kassel; Designed by O. Dodane; Vladimir Turaev
R2,250 Discovery Miles 22 500 Ships in 12 - 17 working days

In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices.

Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines.

Introduction to Combinatorial Torsions (Paperback, 2001 ed.): Vladimir Turaev Introduction to Combinatorial Torsions (Paperback, 2001 ed.)
Vladimir Turaev
R1,562 Discovery Miles 15 620 Ships in 10 - 15 working days

This book is an extended version of the notes of my lecture course given at ETH in spring 1999. The course was intended as an introduction to combinatorial torsions and their relations to the famous Seiberg-Witten invariants. Torsions were introduced originally in the 3-dimensional setting by K. Rei demeister (1935) who used them to give a homeomorphism classification of 3-dimensional lens spaces. The Reidemeister torsions are defined using simple linear algebra and standard notions of combinatorial topology: triangulations (or, more generally, CW-decompositions), coverings, cellular chain complexes, etc. The Reidemeister torsions were generalized to arbitrary dimensions by W. Franz (1935) and later studied by many authors. In 1962, J. Milnor observed 3 that the classical Alexander polynomial of a link in the 3-sphere 8 can be interpreted as a torsion of the link exterior. Milnor's arguments work for an arbitrary compact 3-manifold M whose boundary is non-void and consists of tori: The Alexander polynomial of M and the Milnor torsion of M essentially coincide."

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