Geometry and Topology Seminar

Heegaard Floer homology, for a closed 3-manifold Y, is usually defined by
counting certain holomorphic disks or curves, in a symplectic
manifold coming from a Heegaard decomposition of Y. Recent
developments in bordered Heegaard Floer theory makes it possible to
describe the hat version, HF^(Y), in terms of purely combinatorial and
algebraic constructions. This works by cutting Y along dividing
surfaces into sufficiently simple pieces, then combining the bordered
invariants of each resulting piece, in a way similar in spirit to a
(2+1)-dimensional topological quantum field theory. I will give an
overview of bordered Floer theory and then discuss my work in using it to
give combinatorial constructions.