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The mapping class group action on $\mathsf{SU}(3)$-character varieties

Part of: Noncompact transformation groups Locally compact groups and their algebras Ergodic theory

Published online by Cambridge University Press:  15 June 2020

WILLIAM M. GOLDMAN Open the ORCID record for WILLIAM M. GOLDMAN [Opens in a new window] ,
SEAN LAWTON Open the ORCID record for SEAN LAWTON [Opens in a new window]  and
EUGENE Z. XIA Open the ORCID record for EUGENE Z. XIA [Opens in a new window]
WILLIAM M. GOLDMAN
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA (e-mail: wmg@umd.edu)
SEAN LAWTON
Affiliation:
Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030, USA (e-mail: slawton3@gmu.edu)
EUGENE Z. XIA
Affiliation:
Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan (e-mail: ezxia@ncku.edu.tw)
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Abstract

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Let $\unicode[STIX]{x1D6F4}$ be a compact orientable surface of genus $g=1$ with $n=1$ boundary component. The mapping class group $\unicode[STIX]{x1D6E4}$ of $\unicode[STIX]{x1D6F4}$ acts on the $\mathsf{SU}(3)$-character variety of $\unicode[STIX]{x1D6F4}$. We show that the action is ergodic with respect to the natural symplectic measure on the character variety.

Keywords

character varietyergodicitysimple closed curves

MSC classification

Primary: 22F50: Groups as automorphisms of other structures 22D40: Ergodic theory on groups 37A25: Ergodicity, mixing, rates of mixing
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 8 , August 2021 , pp. 2382 - 2396
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2020. Published by Cambridge University Press

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