
Workshop
on Symplectic Topology
SYMAT05July
7  9, 2005
Instituto Superior Técnico, Lisboa Lectures
by
Denis Auroux
(Massachusetts Institute of Technology)
Fiber sums of Lefschetz fibrations. This talk will be about
Lefschetz fibrations (i.e., fibrations over the 2sphere with at most
nodal fibers), their relation to symplectic 4manifolds, 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 threesphere 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
OzsvathSzabo.
