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Hauptverfasser: Digiosia, Leo, Nelson, Jo
Format: Preprint
Veröffentlicht: 2021
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Online-Zugang:https://arxiv.org/abs/2107.07102
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author Digiosia, Leo
Nelson, Jo
author_facet Digiosia, Leo
Nelson, Jo
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2107_07102
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle A contact McKay correspondence for links of simple singularities
Digiosia, Leo
Nelson, Jo
Symplectic Geometry
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.
title A contact McKay correspondence for links of simple singularities
topic Symplectic Geometry
url https://arxiv.org/abs/2107.07102