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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.

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