IJPAM: Volume 18, No. 2 (2005)

THE NATURAL MAP $B_n \to B_{2n}$

Mohammad N. Abdulrahim
Department of Mathematics
Beirut Arab University
P.O. Box 11-5020, Beirut, LEBANON
e-mail: [email protected]

Abstract.We consider the linear representation of the braid group on $n$ strands by automorphisms of the free group $F_n$; the representation that is discovered by M. Wada. Using the special case of Cohen's map $B_n \to B_{2n}$ and composing it with Wada's embedding $B_{2n} \to \,\text{\rm Aut}\,(F_{2n})$, we get a linear representation of degree $2n$ which has a subrepresentation isomorphic to the well-known Burau representation.

Received: February 23, 2004

AMS Subject Classification: 20F36

Key Words and Phrases: Artin representation, braid group, Burau representation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 18
Issue: 2