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Caltech

Geometry and Topology Seminar

Friday, October 3, 2014
3:00pm to 5:00pm
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Combinatorial constructions of Heegaard Floer homology using bordered invariants.
Bohua Zhan, Instructor, Mathematics, MIT,

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.

For more information, please contact Subhojoy Gupta by email at subhojoy@caltech.edu.