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Abstract
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Consider the kernel
of the Magnus representation of the Torelli group and the kernel
of the Burau representation of the braid group. We prove that for
and for
the
groups
and
have infinite rank first homology. As a consequence we conclude that neither group
has any finite generating set. The method of proof in each case consists
of producing a kind of “Johnson-type” homomorphism to an infinite rank
abelian group, and proving the image has infinite rank. For the case of
, we
do this with the assistance of a computer calculation.
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Keywords
Magnus representation, Burau representation
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Mathematical Subject Classification 2000
Primary: 20F34, 20F36, 57M07
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Publication
Received: 28 October 2009
Accepted: 15 January 2010
Published: 7 April 2010
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