Workshop on Symplectic Topology
July 7 - 9, 2005
Instituto Superior Técnico, Lisboa
Denis Auroux (Massachusetts Institute of Technology)
Fiber sums of Lefschetz fibrations.
This talk will be about Lefschetz fibrations (i.e., fibrations over the 2-sphere with at most nodal fibers), their relation to symplectic 4-manifolds, and their characterization in terms of quasipositive factorizations in mapping class groups. We will discuss the problem of classifying Lefschetz fibrations, and in particular the manner in which it simplifies if fibrations are stabilized by suitable fiber sum operations.
Frederic Bourgeois (Université Libre de Bruxelles)
Fundamental group of the space of tight contact structures on the torus.
Geiges end Gonzalo recently showed that the fundamental group of the space of the tight contact structures on the torus contains an infinite cyclic subgroup. In this joint work with Fabien Ngo, we show that this fundamental group is exactly the subgroup detected by Geiges end Gonzalo. To obtain this result, we refine some techniques involving convex surfaces and bypasses, introduced by Giroux and Honda.
Ciprian Manolescu (Princeton University and CMI)
Specters in Floer theory.
Floer homology is a variant of Morse theory on infinite dimensional spaces, with applications to both symplectic geometry and gauge theory. In this talk I will address the question of whether Floer homology can be understood as the homology of some algebraic topologic object. I will discuss several proposals due to Cohen, Jones, Segal, Furuta, and Douglas, and their respective range of applicability.
Ivan Smith (University of Cambridge)
Symplectic Khovanov cohomology
I will describe joint work with Paul Seidel in which we construct an invariant of links in the three-sphere using Lagrangian Floer cohomology and certain fibre bundles that arise naturally in Lie theory. Conjecturally this invariant gives a geometric model for Khovanov's combinatorial knot invariants. Just as in Khovanov's theory, there are equivariant cousins of the invariant, and there's a relationship to a version of the Heegaard Floer homology of Ozsvath-Szabo.