On the character variety of the three-holed projective plane

2015/09/28 by Sara Maloni, Maloni, Sara, Frederic Palesi +1 · 1 citation
Mathematics · #20E05 #37A15 #57M50 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:20E05 #msc:37A15 #msc:57M50

paper · pdf · doi:10.48550/arxiv.1509.08341

27 pages

arxiv created 2015/09/28 · arxiv updated 2015/09/29

Abstract

We study the (relative) SL(2,C) character varieties of the three-holed projective plane and the action of the mapping class group on them. We describe a domain of discontinuity for this action, which strictly contains the set of primitive stable representations defined by Minsky, and also the set of convex-cocompact characters. We consider the relationship with the previous work of the authors and S. P. Tan on the character variety of the four-holed sphere.

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• Bowditch representations in Gromov-hyperbolic spaces : characterizations, dynamics of Out(\mathbbF₂) and recognition

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