On the character variety of the three-holed projective plane

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.

27 pages

References in corpus (4)

• Dimension of the Torelli group for Out(F_n)
• Dynamics on character varieties: a survey
• Polynomial automorphisms of C^n preserving the Markoff-Hurwitz polynomial
• Simple geodesics and Markoff quads

Cited by in corpus (1)

• On type-preserving representations of the thrice punctured projective plane group