Groups, Geometry, and Dynamics

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Volume 9, Issue 3, 2015, pp. 737–782
DOI: 10.4171/GGD/326

Published online: 2015-10-29

On the character variety of the four-holed sphere

Sara Maloni[1], Frédéric Palesi[2] and Ser Peow Tan[3]

(1) Brown University, Providence, USA
(2) Aix-Marseille Université, Marseille, France
(3) National University of Singapore, Singapore

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.

Keywords: Four-holed sphere, character variety, mapping class group, Bowditch set, domain of discontinuity, Markoff maps

Maloni Sara, Palesi Frédéric, Tan Ser Peow: On the character variety of the four-holed sphere. Groups Geom. Dyn. 9 (2015), 737-782. doi: 10.4171/GGD/326