Inventiones mathematicae

, Volume 142, Issue 3, pp 451–486

The braid group B4 is linear

  • Daan Krammer

DOI: 10.1007/s002220000088

Cite this article as:
Krammer, D. Invent. math. (2000) 142: 451. doi:10.1007/s002220000088


We study a linear representation ρ:Bn? GLm(Z[q±1,t±1]) with m=n(n-1)/2. We will show that for n=4, this representation is faithful. We prove a relation with the new Charney length function. We formulate a conjecture implying that ρ is faithful for all n.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Daan Krammer
    • 1
  1. 1.Mathematical Institute, University of Basle, Rheinsprung 21, 4051 Basle, Switzerland¶(e-mail:

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