Abstract
Gompf (Ann Math (2) 148(2):619–693, 1998) describes a Stein domain structure on the disk cotangent bundle of any closed surface S by a Legendrian handlebody diagram. We prove that Gompf’s Stein domain is symplectomorphic to the disk cotangent bundle equipped with its canonical symplectic structure and the boundary of this domain is contactomorphic to the unit cotangent bundle of S equipped with its canonical contact structure. As a corollary, we obtain a surgery diagram for the canonical contact structure on the unit cotangent bundle of S.
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04 November 2019
After our article entitled “Stein and Weinstein structures on disk cotangent bundles of surfaces” was accepted and appeared online, it was pointed out by Sylvain Courte that our proof of the existence of the symplectomorphisms in Theorem 1.1 is flawed. Our proof of the existence of the contactomorphisms, however, holds true in both parts of Theorem 1.1.
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Acknowledgements
We would like to thank R.E. Gompf and A.I. Stipsicz for helpful comments on a draft of this paper.
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Ozbagci, B. Stein and Weinstein structures on disk cotangent bundles of surfaces. Arch. Math. 113, 661–670 (2019). https://doi.org/10.1007/s00013-019-01357-y
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DOI: https://doi.org/10.1007/s00013-019-01357-y