In this talk we consider the links of simple singularities, which are contactomoprhic to S3/G for finite subgroups G of SU2(ℂ). We explain how to compute the cylindrical contact homology of S3/G by means of perturbing the canonical contact form by a Morse function that is invariant under the corresponding rotation subgroup. We prove that the ranks are given in terms of the number of conjugacy classes of G, demonstrating a form of the McKay correspondence. We also explain how our computation realizes the Seifert fiber structure of these links.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
