Australian Geometric Topology Webinar (AGTW)

AGTW Broadcast 

Date: Wednesday, 4 November 2026 

Time: 12noon-1pm 

Speaker: Lorenzo Ruffoni (Binghamton University) 

Location: We will join the webinar online in SMRI Seminar Room (A12 Macleay Room 301).  

Title: Convex cocompact groups with three-dimensional limit sets 

Abstract: Given a discrete group of isometries of a real hyperbolic space, we can look
at its limit set, i.e., the set of accumulation points of its orbits on the sphere at
infinity.  This is a compact metric space on which the group acts, and which enjoys many
interesting geometric, topological, and dynamical features.  For example, classical
Kleinian groups provide many examples with limit sets that are quasicircles, Cantor
sets, and Sierpinski carpets.  

In this talk, I will discuss how to construct examples whose limit sets are various
low-dimensional trees of manifolds.  In particular, we answer a question of M.
Kapovich, by constructing convex cocompact groups of isometries of real hyperbolic
spaces, whose limit sets are Cech cohomology 3-spheres not homeomorphic to S^3.  These
groups are right-angled Coxeter groups and our construction is flexible enough to
produce infinitely many quasi-isometry classes.  This is joint work with S.  Douba,
G.-S.  Lee, and L.  Marquis.