Knots, Links, Braids and 3-Manifolds: An Introduction to the New Invariants in Low-Dimensional Topology
About this Title
V. V. Prasolov, Moscow, Russia and A. B. Sossinsky, Independent University of Moscow, Moscow, Russia
Publication: Translations of Mathematical Monographs
Publication Year: 1997; Volume 154
ISBNs: 978-0-8218-0898-6 (print); 978-1-4704-4569-0 (online)
MathSciNet review: MR1414898
MSC: Primary 57M25; Secondary 57M12, 57N10
This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its modifications and generalizations, including a mathematical treatment of Jones–Witten invariants. It emphasizes the geometric aspects of the theory and treats topics such as braids, homeomorphisms of surfaces, surgery of $3$-manifolds (Kirby calculus), and branched coverings. This attractive geometric material, interesting in itself yet not previously gathered in book form, constitutes the basis of the last two chapters, where the Jones–Witten invariants are constructed via the rigorous skein algebra approach.
Unlike several other books, where the introduction of all of these invariants requires the sophisticated abstract algebra of quantum groups and representation theory, the mathematical prerequisites in this book are minimal. Numerous figures and problems make it suitable as a course text and for self-study.
Undergraduates, graduate students, research mathematicians and physicists interested in differential geometry.
Table of Contents
- Chapter I. Knots, links, and ribbons
- Chapter II. Knots and link invariants
- Chapter III. Braids
- Chapter IV. 3-manifolds
- Chapter V. Homeomorphisms of surfaces
- Chapter VI. Surgery of 3-manifolds
- Chapter VII. Branched coverings
- Chapter VIII. Skein invariants of 3-manifolds
- Chapter IX. Invariants of links in 3-manifolds