Geometry & Topology
- Geom. Topol.
- Volume 3, Number 1 (1999), 397-404.
The Burau representation is not faithful for $n = 5$
The Burau representation is a natural action of the braid group on the free –module of rank . It is a longstanding open problem to determine for which values of this representation is faithful. It is known to be faithful for . Moody has shown that it is not faithful for and Long and Paton improved on Moody’s techniques to bring this down to . Their construction uses a simple closed curve on the –punctured disc with certain homological properties. In this paper we give such a curve on the –punctured disc, thus proving that the Burau representation is not faithful for .
Geom. Topol., Volume 3, Number 1 (1999), 397-404.
Received: 21 July 1999
Accepted: 23 November 1999
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Bigelow, Stephen. The Burau representation is not faithful for $n = 5$. Geom. Topol. 3 (1999), no. 1, 397--404. doi:10.2140/gt.1999.3.397. https://projecteuclid.org/euclid.gt/1513883152