Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: Continuous motions of limit sets

Presented by Caroline Series , Warwick, (LMS prize 2014 Winner)

22 February 2016 16:00 in CM221

A Kleinian group is a discrete group of isometries of hyperbolic 3-space. Its limit set, contained in the Riemann sphere, is the set of accumulation points of any orbit. In particular the limit set of a hyperbolic surface group F is the unit circle.

If G is a Kleinian group abstractly isomorphic to F, there is an induced map, known as a Cannon-Thurston (CT) map, between their limit sets. More precisely, the CT-map is a continuous equivariant map from the unit circle into the Riemann sphere.

Suppose now F is fixed while G varies. We discuss work with Mahan Mj about the behaviour of the corresponding CT-maps, viewed as maps from the circle to the sphere. We explain how a simple criterion for the existence of a CT-map can be adapted to establish conditions on convergence of a sequence of groups G_n under which the corresponding sequence of CT-maps converges pointwise or uniformly to the expected limit. Very surprisingly, however, under certain circumstances even pointwise convergence may fail.

Contact anna.felikson@durham.ac.uk for more information