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1 February 2016 The modular action on PSL2(R)-characters in genus 2
Julien Marché, Maxime Wolff
Duke Math. J. 165(2): 371-412 (1 February 2016). DOI: 10.1215/00127094-3166522

Abstract

We explore the dynamics of the action of the mapping class group in genus 2 on the PSL2(R)-character variety. We prove that this action is ergodic on the connected components of Euler class ±1, as it was conjectured by Goldman. In the connected component of Euler class 0 there are two invariant open subsets; on one of them the action is ergodic. In this process we give a partial answer to a question posed by Bowditch.

Citation

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Julien Marché. Maxime Wolff. "The modular action on PSL2(R)-characters in genus 2." Duke Math. J. 165 (2) 371 - 412, 1 February 2016. https://doi.org/10.1215/00127094-3166522

Information

Received: 7 December 2013; Revised: 3 February 2015; Published: 1 February 2016
First available in Project Euclid: 19 January 2016

zbMATH: 1353.37056
MathSciNet: MR3457677
Digital Object Identifier: 10.1215/00127094-3166522

Subjects:
Primary: 58D29
Secondary: 20H10 , 30F60 , 57M05

Keywords: Character varieties , ergodicity , mapping class groups

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 2 • 1 February 2016
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