Math 290, Spring 2009
Organizer: Ian Agol
This semester, this seminar will focus on the study of essential
surfaces in 3-manifolds and
related concepts, such as the virtual Haken conjecture, the virtual
positive
first betti number conjecture, and Heegaard gradient. Principally we
will
be interested in the background results for a theorem of Lackenby which
implies that hyperbolic 3-orbifolds with non-trivial vertices in the
singular
locus contain immersed essential surfaces. We will discuss property
(tau),
the Golod-Shafarevich property, and properties of Kleinian groups.
Participants will be expected to give a talk on one of the topics in
the seminar.
Source Papers:
Surface subgroups of Kleinian
groups with torsion
Heegaard
genus and property (tau) for hyperbolic 3-manifolds
LERF and the Lubotzky-Sarnak
conjecture
Free groups in lattices
Covering spaces of
arithmetic 3-orbifolds
Covering spaces of
3-orbifolds
The asymptotic behaviour of
Heegaard genus
Heegaard splittings, the
virtually Haken conjecture and Property (tau)
This paper attempts to construct incompressible surfaces in finite
covering spaces
of a hyperbolic 3-manifold by performing ``weak reductions" of Heegaard
splittings
Large embedded balls and
Heegaard genus in negative curvature
Some of the arguments in this paper (based on pleated surface
interpolation
techniques going back to Thurston) may replace arguments using minimal
surfaces in the previous paper
Heegaard splittings
of compact 3-manifolds
A survey paper on Heegaard splittings by Marty Scharlemann