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The Chillingworth class is a signed stable length

Ingrid Irmer

Algebraic & Geometric Topology 15 (2015) 1863–1876
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
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1017 Academic Way
Tallahassee, FL 32306-4510
USA