Involve: A Journal of Mathematics
- Volume 10, Number 3 (2017), 417-442.
Reeb dynamics of the link of the $A_n$ singularity
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 .
Involve, Volume 10, Number 3 (2017), 417-442.
Received: 18 September 2015
Revised: 7 June 2016
Accepted: 9 June 2016
First available in Project Euclid: 12 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 37B30: Index theory, Morse-Conley indices 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx] 57R17: Symplectic and contact topology
Secondary: 53D42: Symplectic field theory; contact homology
Abbrescia, Leonardo; Huq-Kuruvilla, Irit; Nelson, Jo; Sultani, Nawaz. Reeb dynamics of the link of the $A_n$ singularity. Involve 10 (2017), no. 3, 417--442. doi:10.2140/involve.2017.10.417. https://projecteuclid.org/euclid.involve/1513087847