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＜E-Book＞
Properties of Closed 3-Braids and Braid Representations of Links / by Alexander Stoimenow
(SpringerBriefs in Mathematics. ISSN:21918201)

Edition	1st ed. 2017.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2017
Language	English
Size	X, 110 p. 89 illus : online resource
Authors	*Stoimenow, Alexander author SpringerLink (Online service)
Subjects	LCSH:Topological groups LCSH:Lie groups LCSH:Topology LCSH:Group theory LCSH:Functions of complex variables FREE:Topological Groups and Lie Groups FREE:Topology FREE:Group Theory and Generalizations FREE:Several Complex Variables and Analytic Spaces
Notes	1. Introduction -- 2. Preliminaries, basic definitions and conventions -- 3. Xu’s form and Seifert surfaces -- 4. Polynomial invariants -- 5. Positivity of 3-braid links -- 6. Studying alternating links by braid index -- 7. Applications of the representation theory -- Appendix. –References.-Index 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 HTTP:URL=https://doi.org/10.1007/978-3-319-68149-8

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