Braid Groups, Christian Kassel, Vladimir Turaev



Braid Groups, Christian Kassel, Vladimir Turaev
Springer | English | ISBN 0387338411 | 348 pages | File type: PDF | 6.01 mb | 2008
Braids and braid groups have been at the heart of mathematical development over the last two decades. Braids play an important role in diverse areas of mathematics and theoretical physics. The special beauty of the theory of braids stems from their attractive geometric nature and their close relations to other fundamental geometric objects, such as knots, links, mapping class groups of surfaces, and configuration spaces. In this presentation the authors thoroughly examine various aspects of the theory of braids, starting from basic definitions and then moving to more recent results. The advanced topics cover the Burau and the LawrenceKrammerBigelow representations of the braid groups, the AlexanderConway and Jones link polynomials, connections with the representation theory of the IwahoriHecke algebras, and the Garside structure and orderability of the braid groups.

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