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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Some remarks on the size of tubular neighborhoods in contact topology and fillability

Klaus Niederkrüger and Francisco Presas

Geometry & Topology 14 (2010) 719–754
Abstract

The well-known tubular neighborhood theorem for contact submanifolds states that a small enough neighborhood of such a submanifold N is uniquely determined by the contact structure on N, and the conformal symplectic structure of the normal bundle. In particular, if the submanifold N has trivial normal bundle then its tubular neighborhood will be contactomorphic to a neighborhood of N ×{0} in the model space N × 2k.

In this article we make the observation that if (N,ξN) is a 3–dimensional overtwisted submanifold with trivial normal bundle in (M,ξ), and if its model neighborhood is sufficiently large, then (M,ξ) does not admit a symplectically aspherical filling.

Keywords
neighborhoods of contact submanifolds, fillability
Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 53D35
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
Authors
Klaus Niederkrüger
Klaus Niederkrüger
Institut de mathématiques de Toulouse
Université Paul Sabatier – Toulouse III
31062 Toulouse Cedex 9
France
Francisco Presas
Francisco Presas
ICMAT
CSIC
Facultad de Matematicas
Universidad Complutense de Madrid
Plaza de Ciencias no 3
28040 Madrid
Spain