Embedded contact homology and its applications

Details Embedded contact homology and its applications Embedded contact homology and its applications

2010-03-16

arxiv.org/abs/1003.3209v1

Mathematics

Symplectic Geometry

expository article to accompany invited talk at 2010 ICM

Scientific paper

Embedded contact homology (ECH) is a kind of Floer homology for contact three-manifolds. Taubes has shown that ECH is isomorphic to a version of Seiberg-Witten Floer homology (and both are conjecturally isomorphic to a version of Heegaard Floer homology). This isomorphism allows information to be transferred between topology and contact geometry in three dimensions. In this article we first give an overview of the definition of embedded contact homology. We then outline its applications to generalizations of the Weinstein conjecture, the Arnold chord conjecture, and obstructions to symplectic embeddings in four dimensions.

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