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- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
About this book
This book studies diverse aspects of braid representations via knots and links. Complete classification results are illustrated for several properties through Xu’s normal 3-braid form and the Hecke algebra representation theory of link polynomials developed by Jones. Topological link types are identified within closures of 3-braids which have a given Alexander or Jones polynomial. Further classifications of knots and links arising by the closure of 3-braids are given, and new results about 4-braids are part of the work. Written with knot theorists, topologists,and graduate students in mind, this book features the identification and analysis of effective techniques for diagrammatic examples with unexpected properties.
Keywords
- link polynomial
- positive braid
- strongly quasi-positive link
- Positivity of 3-braid links
- Seifert surface
- Burau representation
- incompressible surface
- Seifert surfaces
- Morton-Franks-Williams bound
- Applications of representation theory
- Recovering the Burau trace
- Mahler measures
- Fibered Dean knots
- Alexander polynomial
- Jones polynomial
- Gauß sum invariants
Reviews
Authors and Affiliations
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School of General Studies, Gwangju Institute of Science and Technology, Gwangju, Korea (Republic of)
Alexander Stoimenow
Bibliographic Information
Book Title: Properties of Closed 3-Braids and Braid Representations of Links
Authors: Alexander Stoimenow
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-68149-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2017
Softcover ISBN: 978-3-319-68148-1Published: 08 December 2017
eBook ISBN: 978-3-319-68149-8Published: 29 November 2017
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: X, 110
Number of Illustrations: 89 b/w illustrations
Topics: Topological Groups, Lie Groups, Topology, Group Theory and Generalizations, Several Complex Variables and Analytic Spaces