ENGLISH

Knots, Links, Braids and 3-Manifolds: An Introduction to the New Invariants in Low-Dimensional Topology (Translations of Mathematical Monographs)

By V. V. Prasolov , A. B. Sossinsky

Book information

Publisher
Amer Mathematical Society
Year
1996
ISBN
0821808982, 9780821808986, 0821805886, 9780821805886
LCC
QA612.14 .P73 1997
Open Library ID
OL18145427M
Language
english
Format
DJVU
Filesize
7 MB (6824210 bytes)
Series
Translations of Mathematical Monographs
Pages
238\238
Time added
2014-10-05 02:30:00

Description

This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent 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 (mainly due to the Saint Petersburg school). Unlike several recent monographs, where all of these invariants are introduced by using the sophisticated abstract algebra of quantum groups and representation theory, the mathematical prerequisites are minimal in this book. Numerous figures and problems make it suitable as a course text and for self-study.

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