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

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

2004-10-04

arxiv.org/abs/math/0410061v3

Geom. Topol. 10 (2006) 169-266

Mathematics

Symplectic Geometry

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

Scientific paper

10.2140/gt.2006.10.169

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).

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