Representations of braid groups
| dc.creator | Bigelow, Stephen | |
| dc.date | 2003-04-15 | |
| dc.date.accessioned | 2026-07-07T04:56:56Z | |
| dc.date.available | 2026-07-07T04:56:56Z | |
| dc.description | In this paper we survey some work on representations of $B_n$ given by the induced action on a homology module of some space. One of these, called the Lawrence-Krammer representation, recently came to prominence when it was shown to be faithful for all $n$. We will outline the methods used, applying them to a closely related representation for which the proof is slightly easier. The main tool is the Blanchfield pairing, a sesquilinear pairing between elements of relative homology. We discuss two other applications of the Blanchfield pairing, namely a proof that the Burau representation is not faithful for large $n$, and a homological definition of the Jones polynomial. Finally, we discuss possible applications to the representation theory of the Hecke algebra, and ultimately of the symmetric group over fields of non-zero characteristic. | |
| dc.identifier | https://arxiv.org/abs/math/0304212 | |
| dc.identifier | http://arxiv.org/abs/math/0304212 | |
| dc.identifier | Proceedings of the ICM, Beijing 2002, vol. 2, 37--46 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67099 | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F36, 20C08 | |
| dc.title | Representations of braid groups | |
| dc.type | text |