Braids, their properties and generalizations

Details Braids, their properties and generalizations Braids, their properties and generalizations

2006-11-22

arxiv.org/abs/math/0611712v1

Published in the Handbook of Algebra, Vol. 4. Edited by M.Hazewinkel. North-Holland, Amsterdam, 2006, pp. 427-465

Mathematics

Group Theory

Scientific paper

In the paper we give a survey on braid groups and subjects connected with them. We start with the initial definition, then we give several interpretations as well as several presentations of these groups. Burau presentation for the pure braid group and the Markov normal form are given next. Garside normal form and his solution of the conjugacy problem are presented as well as more recent results on the ordering and on the linearity of braid groups. Next topics are the generalizations of braids, their homological properties and connections with the other mathematical fields, like knot theory (via Alexander and Markov theorems) and homotopy groups of spheres.

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