Six-point configurations in the hyperbolic plane and ergodicity of the mapping class group

  • Julien Marché

    Université Paris Diderot, Sorbonne Paris Cité, Paris, France
  • Maxime Wolff

    Université Paris Diderot, Sorbonne Paris Cité, Paris, France
Six-point configurations in the hyperbolic plane and ergodicity of the mapping class group cover

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Abstract

Let be the space of isometry classes of ordered sextuples of points in the hyperbolic plane such that the product of the six corresponding rotations of angle is the identity. This space is closely related to the -character variety of the genus 2 surface . In this article we study the topology and the natural symplectic structure on , and we describe the action of the mapping class group of on . This completes the classification of the ergodic components of the character variety in genus 2 initiated in [14].

Cite this article

Julien Marché, Maxime Wolff, Six-point configurations in the hyperbolic plane and ergodicity of the mapping class group. Groups Geom. Dyn. 13 (2019), no. 2, pp. 731–766

DOI 10.4171/GGD/503