New combinatorial computations of embedded contact homology

Princeton/IAS Symplectic Geometry Seminar
Topic:New combinatorial computations of embedded contact homology
Speaker:Keon Choi
Affiliation:University of California, Berkeley
Date:Friday, March 7
Time/Room:1:30pm - 2:30pm/S-101
Video Link:https://video.ias.edu/pisgs/2014/0307-KeonChoi

Embedded contact homology is an invariant of a contact three-manifold, which is recently shown to be isomorphic to Heegaard Floer homology and Seiberg-Witten Floer homology. However, ECH chain complex depends on the contact form on the manifold and the almost complex structure on its symplectization. This fact can be used to extract symplectic geometric information (e.g. ECH capacities) but explicit computation of the chain complexes has been carried out only on a few cases. Extending the work of Hutchings-Sullivan, we combinatorially describe the ECH chain complexes of \(T^3\) with general \(T^2\)-invariant contact forms and certain almost complex structures.