Departmental Colloquium
Richard Canary
University of Michigan
Simple Length Rigidity
Abstract: It is a classical result that the geometry of a closed hyperbolic
surface is completely determined by the lengths of finitely many simple
closed geodesics on the surface. One may reformulate this in algebraic
language, as saying that a discrete, faithful representation of the fundamental
group G of a closed surface S is determined, up to conjugacy, by the spectral radii
of the images of finitely many elements which are represented by simple closed
curves on S.
Hitchin discovered a component of the space of representations of G into PSL(n,R),
which bears many resemblances to the Teichmuller space of all representations of
G into PSL(2,R). We show that Hitchin representations are similarly determined by the
spectral radii of the images of elements represented by simple closed curves.
We obtain a similar result for discrete faithful representations of G into PSL(2,C).
(These results are joint work with Martin Bridgeman and Francois Labourie.)
Friday October 21, 2016 at 3:00 PM in LC F6