Action of the Johnson-Torelli group on representation varieties

Authors:
William M. Goldman and Eugene Z. Xia

Journal:
Proc. Amer. Math. Soc. **140** (2012), 1449-1457

MSC (2010):
Primary 57M05, 22D40, 13P10

Published electronically:
July 26, 2011

MathSciNet review:
2869130

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a compact orientable surface with genus and boundary components . Let . Then the mapping class group of acts on the relative -character variety , comprising conjugacy classes of representations with . This action preserves a symplectic structure on the smooth part of , and the corresponding measure is finite. Suppose and . Let be the subgroup generated by Dehn twists along null homologous simple loops in . Then the action of on is ergodic for almost all .

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Additional Information

**William M. Goldman**

Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742

Email:
wmg@math.umd.edu

**Eugene Z. Xia**

Affiliation:
Department of Mathematics, National Center for Theoretical Sciences, National Cheng-kung University, Tainan 701, Taiwan

Email:
ezxia@ncku.edu.tw

DOI:
https://doi.org/10.1090/S0002-9939-2011-10972-9

Received by editor(s):
April 26, 2010

Received by editor(s) in revised form:
December 24, 2010

Published electronically:
July 26, 2011

Additional Notes:
The first author gratefully acknowledges partial support by National Science Foundation grant DMS070781.

The second author gratefully acknowledges partial support by the National Science Council, Taiwan, with grants 96-2115-M-006-002 and 97-2115-M-006-001-MY3.

Communicated by:
Bryna Kra

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.