A contact McKay correspondence for links of simple singularities

Leo Digiosia; Jo Nelson

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arXiv · 2107.07102

A contact McKay correspondence for links of simple singularities

Leo Digiosia·Jo Nelson

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Abstract

We compute the cylindrical contact homology of the links of the simple singularities. These manifolds are contactomorphic to $S^3/G$ for finite subgroups $G\subset SU(2)$. We perturb the degenerate contact form on $S^3/G$ with a Morse function, which is invariant under the corresponding $H\subset SO(3)$ action on $S^2$, to achieve nondegeneracy up to an action threshold. The cylindrical contact homology is recovered by taking a direct limit of the action filtered homology groups. The ranks of this homology are given in terms of $|\text{Conj}(G)|$, demonstrating a Floer theoretic McKay correspondence.

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Leo Digiosia, Jo Nelson. 2021-07-15. A contact McKay correspondence for links of simple singularities. https://arxiv.org/abs/2107.07102

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