April 30, 2007
Chris Wendl (MIT): Intersection Theory and Compactness for Holomorphic Curves in Low Dimensions
Abstract:
I will explain a recent result strengthening the standard compactness
theorem for a geometrically natural class of embedded holomorphic
curves in contact 3-manifolds: it turns out the intersection theory of
punctured holomorphic curves can be used to rule out multiple covers in
the limit, so that transversality is never a problem. This has
applications to the theory of finite energy foliations, as well as
suggesting an approach for defining distinctly "low dimensional"
versions of Contact Homology and SFT. I will also describe some
related results in symplectic 4-manifolds and nontrivial symplectic
cobordisms, which are part of a larger program to justify the statement
that "nice holomorphic curves degenerate nicely".
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