Geometry & Topology

A class of non-fillable contact structures

Francisco Presas

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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.

Article information

Geom. Topol., Volume 11, Number 4 (2007), 2203-2225.

Received: 16 January 2007
Revised: 2 September 2007
Accepted: 9 August 2007
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R17: Symplectic and contact topology
Secondary: 53D10: Contact manifolds, general

contact structures fillings


Presas, Francisco. A class of non-fillable contact structures. Geom. Topol. 11 (2007), no. 4, 2203--2225. doi:10.2140/gt.2007.11.2203.

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