Geometry/Topology Seminar
Colin Davalo
Heidelberg University
Finite-sided Dirichlet domains for Anosov representations
Abstract: Dirichlet domains provide polyhedral fundamental domains for discrete
subgroups of the isometries of hyperbolic space on the hyperbolic space.
Selberg introduced a similar construction of a polyhedral fundamental
domain for the action of discrete subgroups of the higher rank Lie group
SL(n,R) on the projective model of the associated symmetric space. His
motivation was to study uniform lattices, for which these domains are
finite-sided. We will address the following question asked
by Kapovich: for which Anosov subgroups are these domains finite-sided ?
Anosov subgroups are hyperbolic discrete subgroups satisfying strong
dynamical properties that have infinite covolume in higher rank. We will
first consider an example of an Anosov subgroup for which this
fundamental domain can have infinitely many sides. We then provide a
sufficient condition on a subgroup to ensure that the domain is finitely
sided in a strong sense. This is joint work with Max Riestenberg.
Note unusual time/room
Monday February 26, 2024 at 3:00 PM in 427 SEO