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Braids and Knots

  • Patrick D. BangertEmail author
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Part of the Lecture Notes in Mathematics book series (LNM, volume 1973)

Abstract

We introduce braids via their historical roots and uses, make connections with knot theory and present the mathematical theory of braids through the braid group. Several basic mathematical properties of braids are explored and equivalence problems under several conditions defined and partly solved. The connection with knots is spelled out in detail and translation methods are presented. Finally a number of applications of braid theory are given. The presentation is pedagogical and principally aimed at interested readers from different fields of mathematics and natural science. The discussions are as self-contained as can be expected within the space limits and require very little previous mathematical knowledge. Literature references are given throughout to the original papers and to overview sources where more can be learned.

Keywords

Word Problem Braid Group Critical Pair Conjugacy Problem Jones Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Mathematisch InstituutGermany

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