Knots, links, braids and 3-manifolds : an introduction to the new invariants in low-dimensional topology

Author(s)

• Prasolov, V. V.
• Sosinskiĭ, A. B. (Alekseĭ Bronislavovich)

Bibliographic Information

Knots, links, braids and 3-manifolds : an introduction to the new invariants in low-dimensional topology

V.V. Prasolov, A.B. Sossinsky ; [translated by A.B. Sossinsky from an original Russian manuscript]

（Translations of mathematical monographs, v. 154）

American Mathematical Society, c1997

• :
• : pbk

Other Title

Knots, links, braids, and three-manifolds

Note

Includes bibliographical references (p. 231-236) and index

Description and Table of Contents

Volume

: ISBN 9780821805886

Description

This book is intended for researchers working in geometry and topology.

Volume

: pbk ISBN 9780821808986

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.

Table of Contents

Knots, links, and ribbons Knot and link invariants Braids 3-manifolds Homeomorphisms of surfaces Surgery of 3-manifolds Branched coverings Skein invariants of 3-manifolds Invariants of links in 3-manifolds Appendix Solutions References Index.

by "Nielsen BookData"

Details

• NCID: BA28796930
• ISBN:
  • 0821805886
  • 0821808982
• LCCN: 96022164
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: rus
• Place of Publication: Providence, R.I.
• Pages/Volumes: viii, 239 p.
• Size: 27 cm
• Classification:
  • LCC : QA612.14
  • DC20 : 514/.2
  • NDC8 : 415.7
• Subject Headings:
  • LCSH : Low-dimensional topology
• Parent Bibliography ID:
  • BA00080309