#### Volume 11, issue 4 (2007)

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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 ${S}^{3}×{\prod }_{j}{\Sigma }_{j}$, for $g\left({\Sigma }_{j}\right)\ge 2$, possesses this kind of contact structure and so any connected sum with those manifolds also does it.

##### Keywords
contact structures, fillings
Primary: 57R17
Secondary: 53D10