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The Magnus representation of the Torelli group $\mathcal{I}_{g,1}$ is not faithful for $g \geq 2$


Author: Masaaki Suzuki
Journal: Proc. Amer. Math. Soc. 130 (2002), 909-914
MSC (2000): Primary 57M05; Secondary 20F34, 57N05
Published electronically: June 8, 2001
MathSciNet review: 1866048
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Abstract:

In this paper we consider the Magnus representation of the Torelli group. We prove that it is not faithful by showing a non-trivial element in the kernel of this representaion.


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Additional Information

Masaaki Suzuki
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan
Email: macky@ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-01-06128-7
Keywords: Magnus representation, mapping class group, Torelli group
Received by editor(s): May 16, 2000
Received by editor(s) in revised form: August 30, 2000
Published electronically: June 8, 2001
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2001 American Mathematical Society