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Factoring in the hyperelliptic Torelli group†

Published online by Cambridge University Press:  19 June 2015

TARA E. BRENDLE  and
DAN MARGALIT
TARA E. BRENDLE
Affiliation:
School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, Glasgow G12 8QW, e-mail: [email protected]
DAN MARGALIT
Affiliation:
School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332U.S.A. e-mail: [email protected]
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Abstract

The hyperelliptic Torelli group is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface and that also commute with some fixed hyperelliptic involution. Putman and the authors proved that this group is generated by Dehn twists about separating curves fixed by the hyperelliptic involution. In this paper, we introduce an algorithmic approach to factoring a wide class of elements of the hyperelliptic Torelli group into such Dehn twists, and apply our methods to several basic types of elements. As one consequence, we answer an old question of Dennis Johnson.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 159 , Issue 2 , September 2015 , pp. 207 - 217
Copyright
Copyright © Cambridge Philosophical Society 2015 

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Footnotes

†

Supported in part by EPSRC grant EP/J019593/1. Supported by the Sloan Foundation and the NSF Grant No. DMS - 1057874.

References

REFERENCES

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