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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.

Geometry and Topology Seminar: Two-systoles of hyperbolic three-manifolds.

Presented by Misha Belolipetsky,

28 April 2016 13:00 in CM 221.

I will discuss the geometry of incompressible and, more generally,
\pi_1-injective surfaces in closed hyperbolic 3-manifolds. By a
result of Kahn-Markovic we know that such surfaces are always
present, and that there are plenty of them. We investigate the
relation between the genus and the area of \pi_1-injective surfaces
and geometric invariants of the ambient manifold such as its volume,
Heegard genus and systole. As an application, we prove that the
free-rank of the fundamental groups of the congruence covers of
an arithmetic hyperbolic 3-manifold grows polynomially with
volume.

Contact mark.a.powell@durham.ac.uk or andrew.lobb@durham.ac.uk or wilhelm.klingenberg@durham.ac.uk for more information