Volume 11, issue 4 (2007)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A class of non-fillable contact structures

Francisco Presas

Geometry & Topology 11 (2007) 2203–2225

arXiv: math.SG/0611390

Abstract

A geometric obstruction, the so called “PS–structure”, for a contact structure to not being fillable has been found by Niederkrüger. This generalizes somehow the concept of overtwisted structure to dimensions higher than 3. This paper elaborates on the theory showing a big number of closed contact manifolds having a "PS–structure". So, they are the first examples of non-fillable high dimensional closed contact manifolds. In particular we show that S3 × jΣj, for g(Σj) 2, possesses this kind of contact structure and so any connected sum with those manifolds also does it.

Keywords
contact structures, fillings
Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 53D10
References
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Publication
Received: 16 January 2007
Revised: 2 September 2007
Accepted: 9 August 2007
Published: 14 November 2007
Proposed: Yasha Eliashberg
Seconded: Peter Oszváth, Leonid Polterovich
Authors
Francisco Presas
Departamento de Matemáticas
Consejo Superior de Investigaciones Científicas
28006 Madrid
Spain