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Archiv der Mathematik

, Volume 113, Issue 6, pp 661–670 | Cite as

Stein and Weinstein structures on disk cotangent bundles of surfaces

  • Burak OzbagciEmail author
Article

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.

Keywords

Stein structure Contact structure Cotangent bundle Weinstein structure Surgery diagram 

Mathematics Subject Classification

57R17 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsKoç UniversityIstanbulTurkey

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