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