TY  - BOOK
AU  - Turaev,V.G.
TI  - Quantum Invariants of Knots and 3-Manifolds
T2  - De Gruyter Studies in Mathematics
SN  - 9783110435238
AV  - QC174.52.C66 T87 2016
U1  - 514.2 23
PY  - 2016///]
CY  - Berlin
PB  - De Gruyter
KW  - Quantum field theory
KW  - Knot theory
KW  - Three-manifolds (Topology)
KW  - Invariants
KW  - Mathematical physics
KW  - Théorie quantique des champs
KW  - Théorie des nœuds
KW  - Variétés topologiques à 3 dimensions
KW  - Physique mathématique
KW  - MATHEMATICS
KW  - Topology
KW  - bisacsh
KW  - fast
KW  - Electronic books
N1  - 2. Underlying ribbon category; Includes bibliographical references and index; Preface ; Contents ; Introduction ; Part I. Towards Topological Field Theory ; Chapter I. Invariants of graphs in Euclidean 3-space ; 1. Ribbon categories ; 2. Operator invariants of ribbon graphs ; 3. Reduction of Theorem 2.5 to lemmas ; 4. Proof of lemmas ; Notes; Chapter II. Invariants of closed 3-manifolds 1. Modular tensor categories ; 2. Invariants of 3-manifolds ; 3. Proof of Theorem 2.3.2. Action of SL(2; Z) ; 4. Computations in semisimple categories ; 5. Hermitian and unitary categories ; Notes; Chapter III. Foundations of topological quantum field theory 1. Axiomatic definition of TQFT's ; 2. Fundamental properties ; 3. Isomorphisms of TQFT's ; 4. Quantum invariants ; 5. Hermitian and unitary TQFT's ; 6. Elimination of anomalies ; Notes; Chapter IV. Three-dimensional topological quantum field theory 1. Three-dimensional TQFT: preliminary version ; 2. Proof of Theorem 1.9 ; 3. Lagrangian relations and Maslov indices ; 4. Computation of anomalies ; 5. Action of the modular groupoid ; 6. Renormalized 3-dimensional TQFT; 7. Computations in the renormalized TQFT 8. Absolute anomaly-free TQFT ; 9. Anomaly-free TQFT ; 10. Hermitian TQFT ; 11. Unitary TQFT ; 12. Verlinde algebra ; Notes ; Chapter V. Two-dimensional modular functors ; 1. Axioms for a 2-dimensional modular functor
N2  - The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob
UR  - https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1289697
ER  -