Geometry & Topology
- Geom. Topol.
- Volume 10, Number 1 (2006), 169-266.
Rounding corners of polygons and the embedded contact homology of $T^3$
Michael Hutchings and Michael G Sullivan
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 –holomorphic curves in the symplectization. We show that the ECH of 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 .
Article information
Source
Geom. Topol., Volume 10, Number 1 (2006), 169-266.
Dates
Received: 5 October 2004
Accepted: 25 January 2006
First available in Project Euclid: 20 December 2017
Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799706
Digital Object Identifier
doi:10.2140/gt.2006.10.169
Mathematical Reviews number (MathSciNet)
MR2207793
Zentralblatt MATH identifier
1101.53053
Keywords
embedded contact homology Floer homology
Citation
Hutchings, Michael; Sullivan, Michael G. Rounding corners of polygons and the embedded contact homology of $T^3$. Geom. Topol. 10 (2006), no. 1, 169--266. doi:10.2140/gt.2006.10.169. https://projecteuclid.org/euclid.gt/1513799706