Quantum Invariants of Knots and 3-Manifolds / Vladimir G. Turaev.

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.

2. Underlying ribbon category.

Includes bibliographical references and index.

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Online resource; title from digital title page (viewed on August 27, 2019).

English.

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