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Some remarks on the size
of tubular neighborhoods in contact topology and
fillability
Klaus Niederkrüger and Francisco Presas |
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Geometry & Topology 14 (2010) 719–754
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Abstract |
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The well-known tubular neighborhood theorem for contact submanifolds states that a small enough neighborhood of such a submanifold is uniquely determined by the contact structure on , and the conformal symplectic structure of the normal bundle. In particular, if the submanifold has trivial normal bundle then its tubular neighborhood will be contactomorphic to a neighborhood of in the model space . In this article we make the observation that if is a –dimensional overtwisted submanifold with trivial normal bundle in , and if its model neighborhood is sufficiently large, then does not admit a symplectically aspherical filling. |
Keywords
neighborhoods of contact submanifolds, fillability
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Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 53D35
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References |
Publication
Received: 19 March 2009
Revised: 11 November 2009
Accepted: 5 November 2009
Published: 16 February 2010
Proposed: Leonid Polterovich
Seconded: Danny Calegari and Yasha Eliashberg
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Authors |
| Klaus Niederkrüger | |
| Klaus Niederkrüger Institut de mathématiques de Toulouse Université Paul Sabatier – Toulouse III 31062 Toulouse Cedex 9 France |
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| Francisco Presas | |
| Francisco Presas ICMAT CSIC Facultad de Matematicas Universidad Complutense de Madrid Plaza de Ciencias no 3 28040 Madrid Spain |
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