Rounding corners of polygons and the embedded contact homology of T^3

Abstract

The embedded contact homology (ECH) of a 3-manifold with a contact form is a variant of Eliashberg-Givental-Hofer's symplectic field theory, which counts certain embedded J-holomorphic curves in the symplectization. We show that the ECH of T^3 is computed by a combinatorial chain complex which is generated by labeled convex polygons in the plane with vertices at lattice points, and whose differential involves `rounding corners'. We compute the homology of this combinatorial chain complex. The answer agrees with the Ozsvath--Szabo Floer homology HF^+(T^3).

This is the version published by Geometry & Topology on 26 March 2006

References in corpus (2)

• The periodic Floer homology of a Dehn twist
• Homologie de contact des varietes toroidales

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