Mathematics Colloquia and Seminars

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Contact topology is the study of geometric structures on odd dimensional smooth manifolds given by a hyperplane field specified by a one form which satisfies a maximum nondegeneracy condition called complete non-integrability. The associated one form is called a contact form and uniquely determines a vector field called the Reeb vector field on the manifold. I will explain how one to make use of pseudoholomorphic curves to obtain a couple of related varieties of Floer theoretic contact invariants whose chain complexes are generated by Reeb orbits. In particular, I will explain some pitfalls and joint work with Hutchings which circumvents the usual troubles associated with defining contact homology.