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June 2014 The Canonical Contact Structure on the Link of a Cusp Singularity
Naohiko KASUYA
Tokyo J. Math. 37(1): 1-20 (June 2014). DOI: 10.3836/tjm/1406552427


Caubel, Nemethi, and Popescu-Pampu in [2] proved that an oriented 3-manifold admits at most one positive contact structure which can be realized as the complex tangency along the link of a complex surface singularity. They call it the Milnor fillable contact structure. Lekili and Ozbagci in [10] showed that a Milnor fillable contact structure is universally tight. In particular, by Honda's classification [5], the link of a cusp singularity is contactomorphic to the positive contact structure associated to the Anosov flow on a Sol-manifold (see [1]). We describe the contact structure on the link of a cusp singularity in two different ways without using Honda's classification theorem. One description is based on the toric method introduced in Mori [15]. The other description is based on Hirzebruch's construction of the Hilbert modular cusps. Consequently, we give certain answers to the problems in Mori [14] concerning the relation between the cusp singularities and the simple elliptic singularities, and the higher dimensional extension of the local Lutz-Mori twist.


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Naohiko KASUYA. "The Canonical Contact Structure on the Link of a Cusp Singularity." Tokyo J. Math. 37 (1) 1 - 20, June 2014.


Published: June 2014
First available in Project Euclid: 28 July 2014

zbMATH: 1307.57016
MathSciNet: MR3238328
Digital Object Identifier: 10.3836/tjm/1406552427

Primary: 57R17
Secondary: 32S25

Rights: Copyright © 2014 Publication Committee for the Tokyo Journal of Mathematics


Vol.37 • No. 1 • June 2014
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