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Reeb dynamics
of the link of the $A_n$ singularity
Leonardo Abbrescia, I. Huq-Kuruvilla, J. Nelson and N. Sultani |
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Vol. 10 (2017), No. 3, 417–442
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Abstract |
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The link of the singularity, admits a natural contact structure coming from the set of complex tangencies. The canonical contact form associated to is degenerate and thus has no isolated Reeb orbits. We show that there is a nondegenerate contact form for a contact structure equivalent to that has two isolated simple periodic Reeb orbits. We compute the Conley–Zehnder index of these simple orbits and their iterates. From these calculations we compute the positive -equivariant symplectic homology groups for . In addition, we prove that is contactomorphic to the lens space , equipped with its canonical contact structure . |
Keywords
contact geometry, contact topology, Conley–Zehnder index,
$A_n$ singularity, Reeb dynamic, Maslov index
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Mathematical Subject Classification 2010
Primary: 37B30, 53D35, 57R17
Secondary: 53D42
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Milestones
Received: 18 September 2015
Revised: 7 June 2016
Accepted: 9 June 2016
Published: 14 December 2016
Communicated by Colin Adams
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Authors |
| Leonardo Abbrescia | |
| Department of Mathematics Michigan State University 1016 Chester Rd. Apt. B14 Lansing, MI 48912 United States |
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| I. Huq-Kuruvilla | |
| Department of Mathematics Columbia University 2920 Broadway 6580 Lerner Hall New York, NY 10027 United States |
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| J. Nelson | |
| Institute for Advanced Study Columbia University 2990 Broadway Room 509, MC 4403 New York, NY 10027 United States |
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| N. Sultani | |
| Department of Mathematics Columbia University 2920 Broadway 6580 Lerner Hall New York, NY 10027 United States |
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| © 2017 MSP (Mathematical Sciences Publishers). |
