Abstract
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 .
Citation
Stephen Bigelow. "The Burau representation is not faithful for $n = 5$." Geom. Topol. 3 (1) 397 - 404, 1999. https://doi.org/10.2140/gt.1999.3.397
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