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Quantum Invariants: A Study Of Knots, 3-manifolds, And Their Sets

Quantum Invariants: A Study Of Knots, 3-manifolds, And Their Sets
Author: Tomotada Ohtsuki
Publisher: World Scientific
Total Pages: 508
Release: 2001-12-21
Genre: Mathematics
ISBN: 9814490717

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This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The Chern-Simons field theory and the Wess-Zumino-Witten model are described as the physical background of the invariants.


Sir Michael Atiyah

Sir Michael Atiyah
Author: Michael Francis Atiyah
Publisher: American Mathematical Society(RI)
Total Pages: 416
Release: 1998
Genre: Mathematics
ISBN:

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A concis, yet comprehensive introduction to the contemporary politics of Latin America, this book focuses on the enduring difficulties of achieving democratic stability. It explores the conduct of government through classic concepts like authority, accountability, and participation. These themes are developed within a comparative perspective.


Geometry and Physics

Geometry and Physics
Author: H. Pedersen
Publisher: CRC Press
Total Pages: 772
Release: 1996-10-11
Genre: Mathematics
ISBN: 9780824797911

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"Based on the proceedings of the Special Session on Geometry and Physics held over a six month period at the University of Aarhus, Denmark and on articles from the Summer school held at Odense University, Denmark. Offers new contributions on a host of topics that involve physics, geometry, and topology. Written by more than 50 leading international experts."


Research Report

Research Report
Author: Søren Kold Hansen
Publisher:
Total Pages:
Release: 2003
Genre:
ISBN:

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Introduction to Vassiliev Knot Invariants

Introduction to Vassiliev Knot Invariants
Author: S. Chmutov
Publisher: Cambridge University Press
Total Pages: 521
Release: 2012-05-24
Genre: Mathematics
ISBN: 1107020832

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A detailed exposition of the theory with an emphasis on its combinatorial aspects.