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1 April 2002 The topological IHX relation, pure braids, and the Torelli group
Sylvain Gervais, Nathan Habegger
Duke Math. J. 112(2): 265-280 (1 April 2002). DOI: 10.1215/S0012-9074-02-11222-8

Abstract

We prove that the filtration on the pure braid group on g strands, induced by the lower central series of the Torelli group of a genus g surface with one boundary component, coincides with its lower central series, shifted by one.

In particular, the cubic Jacobi relations in the pure braid group are quadratic relations in the Torelli group.

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Sylvain Gervais. Nathan Habegger. "The topological IHX relation, pure braids, and the Torelli group." Duke Math. J. 112 (2) 265 - 280, 1 April 2002. https://doi.org/10.1215/S0012-9074-02-11222-8

Information

Published: 1 April 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1023.20020
MathSciNet: MR1894361
Digital Object Identifier: 10.1215/S0012-9074-02-11222-8

Subjects:
Primary: 57M27
Secondary: 20F36, 20F38, 57R50

Rights: Copyright © 2002 Duke University Press

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Vol.112 • No. 2 • 1 April 2002
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