Geodesic
On the character variety of the four-holed sphere
Sara Maloni1 orcid ; Frédéric Palesi2 ; Ser Peow Tan3
1Brown University, Providence, USA
2Aix-Marseille Université, Marseille, France
3National University of Singapore, Singapore
Groups, geometry, and dynamics, Tome 9 (2015) no. 3, pp. 737-782

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DOI

We study the (relative) SL$(2, \mathbb C) character varieties of the four-holed sphere and the action of the mapping class group on them. We describe a domain of discontinuity for this action, and, in the case of real characters, show that this domain of discontinuity may be non-empty on the components where the relative Euler class is non-maximal.
DOI : 10.4171/ggd/326
Classification : 57-XX, 20-XX, 37-XX
Mots-clés : Four-holed sphere, character variety, mapping class group, Bowditch set, domain of discontinuity, Markoff maps

Sara Maloni  1   ; Frédéric Palesi  2   ; Ser Peow Tan  3

1 Brown University, Providence, USA
2 Aix-Marseille Université, Marseille, France
3 National University of Singapore, Singapore 
Sara Maloni; Frédéric Palesi; Ser Peow Tan. On the character variety of the four-holed sphere. Groups, geometry, and dynamics, Tome 9 (2015) no. 3, pp. 737-782. doi: 10.4171/ggd/326
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     year = {2015},
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     doi = {10.4171/ggd/326},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/326/}
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