The Lawrence-Krammer representation
| dc.creator | Bigelow, Stephen | |
| dc.date | 2002-04-04 | |
| dc.date.accessioned | 2026-07-07T04:47:26Z | |
| dc.date.available | 2026-07-07T04:47:26Z | |
| dc.description | The 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 $H_2(\tilde{C})$ over the ring of Laurent polynomials in $q$ and $t$. In this paper we describe some surfaces in $\tilde{C}$ representing elements of homology. We use these to give a new proof that $H_2(\tilde{C})$ 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. | |
| dc.description | 20 pages, 9 figures | |
| dc.identifier | https://arxiv.org/abs/math/0204057 | |
| dc.identifier | http://arxiv.org/abs/math/0204057 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63717 | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F36; 20C08 | |
| dc.title | The Lawrence-Krammer representation | |
| dc.type | text |