Properties of Closed 3-Braids and Braid Representations of Links

Nonfiction, Science & Nature, Mathematics, Group Theory, Topology
Cover of the book Properties of Closed 3-Braids and Braid Representations of Links by Alexander Stoimenow, Springer International Publishing
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Author: Alexander Stoimenow ISBN: 9783319681498
Publisher: Springer International Publishing Publication: November 29, 2017
Imprint: Springer Language: English
Author: Alexander Stoimenow
ISBN: 9783319681498
Publisher: Springer International Publishing
Publication: November 29, 2017
Imprint: Springer
Language: English

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.

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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.

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