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G&T Monographs |
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Rounding corners of polygons and the embedded contact
homology of T³
Michael Hutchings and Michael C Sullivan
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Geometry & Topology 10 (2006)
169–266
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Abstract
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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).
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Keywords
embedded contact homology, Floer
homology
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Mathematical Subject Classification
Primary: 57R58
Secondary: 57M27
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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
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