|9:30 - 10:30
|11:00 - 12:00
|14:00 - 15:00
|15:30 - 16:30
The rank vs Heegaard genus conjecture says that the Heegaard genus of a
hyperbolic 3-manifold equals the minimal number of generators of its
fundamental group. We show how this relates to a distinguished problem in
topological dynamics, the fixed price problem. The relation is established
using profinite actions.
We compute the contact invariants of all tight contact
structures on the manifolds -Sigma (2,3,6n-1). This is a joint work
with Jeremy Van Horn-Morris.
I will discuss what kind of geometric information
one can get about a sutured manifold using the Spin^c grading on its
sutured Floer homology.
(joint work with T. Etgu) Recently, Honda, Kazez and Matic described an adapted partial open book decomposition of a compact contact 3-manifold with convex boundary by generalizing the work of Giroux in the closed case. This description induces a map from isomorphism classes of compact contact 3-manifolds with convex boundaries to isomorphism classes of partial open book decompositions modulo positive stabilization. We construct the inverse of this map by describing a compact contact 3-manifold with convex boundary compatible with an abstract partial open book decomposition. Consequently, combined with the work of Honda, Kazez and Matic, we obtain a relative version of Giroux correspondence.
- We show that every 3--manifold admits a Heegaard diagram in which
a truncated version of Heegaard Floer homology (when the holomorpic
disks pass through the basepoints at most once) can be computed
combinatorially. The construction relies on the fact that a closed
3--manifold can be given as a triple branched cover of S^3 along a