Geometry & Topology 10 (2006) 169–266

DOI: 10.2140/gt.2006.10.169

arXiv: math.SG/0410061

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 T³ 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 Ozsváth–Szabó Floer homology HF⁺(T³).

Keywords

embedded contact homology, Floer homology

Mathematical Subject Classification

Primary: 57R58

Secondary: 57M27

References

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Publication

Received: 5 October 2004
Accepted: 25 January 2006
Published: 26 March 2006
Proposed: Robion Kirby
Seconded: Peter Ozsváth, Tomasz Mrowka

Authors