Monthly Archives: November 2013

Problem with cylindrical cobordism maps fixed?

In a previous post, I discussed the problem of defining cylindrical contact homology for a contact three-manifold with no contractible Reeb orbits. (In that post I assumed for simplicity that there are no bad Reeb orbits, but I will allow … Continue reading

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Hidden branched covers of trivial cylinders

I would now like to explain another ECH-type trick, which I have been meaning to write about here for a while, and which may have applications to other kinds of contact homology in three dimensions and holomorphic curve counts in … Continue reading

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Non-equivariant contact homology

In a previous post, I explained how that the transversality difficulties in defining cylindrical contact homology can be resolved by using -dependent almost complex structures, but at the expense of obtaining the wrong theory. The theory that one naturally obtains … Continue reading

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What is the geometric meaning of ECH capacities?

Last week, Keon Choi, Dan Cristofaro-Gardiner, David Frenkel, Vinicius Ramos, and I posted a new paper, Symplectic embeddings into four-dimensional concave toric domains. To explain what concave toric domains are, recall that if is a domain in the first quadrant … Continue reading

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