The Chillingworth class is a signed stable length

Irmer, Ingrid

doi:10.2140/agt.2015.15.1863

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ISSN (electronic): 1472-2739

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The Chillingworth class is a signed stable length

Ingrid Irmer

Algebraic & Geometric Topology 15 (2015) 1863–1876

DOI: 10.2140/agt.2015.15.1863

Abstract

An orientation is defined on a family of curve graphs on which the Torelli group acts. It is shown that the resulting signed stable length of an element of the Torelli group is a cohomology class. This cohomology class is half the dual of the contraction of the Johnson homomorphism, the so-called “Chillingworth class”.

Keywords

Mapping class group, curve complexes, Johnson homomorphism

Mathematical Subject Classification 2010

Primary: 20J05

Secondary: 47B47

References

Publication

Received: 18 December 2013

Revised: 3 September 2014

Accepted: 4 November 2014

Published: 10 September 2015

Authors

Ingrid Irmer
Department of Mathematics Florida State University 208 Love Building 1017 Academic Way Tallahassee, FL 32306-4510 USA

Volume 15, issue 4 (2015)