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arXiv · 0909.4825

Infinite generation of the kernels of the Magnus and Burau representations

Thomas Church·Benson Farb
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Abstract

Consider the kernel Mag_g of the Magnus representation of the Torelli group and the kernel Bur_n of the Burau representation of the braid group. We prove that for g >= 2 and for n >= 6 the groups Mag_g and Bur_n 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 Bur_n, we do this with the assistance of a computer calculation.

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BibTeXRIS

Thomas Church, Benson Farb. 2009-09-26. Infinite generation of the kernels of the Magnus and Burau representations. https://doi.org/10.2140/agt.2010.10.837

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