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23 April 2024
 
  » arxiv » math.GT/0204057

 Article overview


The Lawrence-Krammer representation
Stephen Bigelow ;
Date 4 Apr 2002
Subject Geometric Topology MSC-class: 20F36; 20C08 | math.GT
AbstractThe Lawrence-Krammer representation of the braid groups recently came to prominence when it was shown to be faithful by myself and Krammer. It is an action of the braid group on a certain homology module $H_2( ilde{C})$ over the ring of Laurent polynomials in $q$ and $t$. In this paper we describe some surfaces in $ ilde{C}$ representing elements of homology. We use these to give a new proof that $H_2( ilde{C})$ is a free module. We also show that the $(n-2,2)$ representation of the Temperley-Lieb algebra is the image of a map to relative homology at $t=-q^{-1}$, clarifying work of Lawrence.
Source arXiv, math.GT/0204057
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