The structure of relatively hyperbolic groups in convex real projective geometry

2022/03/30 by Islam, Mitul, Zimmer, Andrew
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2203.16596

Abstract

In this paper we prove a general structure theorem for relatively hyperbolic groups (with arbitrary peripheral subgroups) acting naive convex co-compactly on properly convex domains in real projective space. We also establish a characterization of such groups in terms of the existence of an invariant collection of closed unbounded convex subsets with good isolation properties. This is a real projective analogue of results of Hindawi-Hruska-Kleiner for \rm CAT(0) spaces. We also obtain an equivariant homeomorphism between the Bowditch boundary of the group and a quotient of the ideal boundary.

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• Divisible convex sets with properly embedded cones
• Combining relatively hyperbolic groups over a complex of groups
• Constructing Bowditch boundaries of some relatively hyperbolic groups that are homeomorphic to the n-dimensional Sierpiński carpet
• Cusped spaces and quasi-isometries of relatively hyperbolic groups