Geometry & Topology

A class of non-fillable contact structures

Francisco Presas

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799980

Digital Object Identifier
doi:10.2140/gt.2007.11.2203

Mathematical Reviews number (MathSciNet)
MR2372846

Zentralblatt MATH identifier
1132.57023

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

Keywords
contact structures fillings

Citation

Presas, Francisco. A class of non-fillable contact structures. Geom. Topol. 11 (2007), no. 4, 2203--2225. doi:10.2140/gt.2007.11.2203. https://projecteuclid.org/euclid.gt/1513799980


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