A class of non-fillable contact structures

Presas, Francisco

doi:10.2140/gt.2007.11.2203

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

A class of non-fillable contact structures

Francisco Presas

Geometry & Topology 11 (2007) 2203–2225

DOI: 10.2140/gt.2007.11.2203

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 $S^{3} \times \prod_{j} Σ_{j}$ , for $g (Σ_{j}) \geq 2$ , 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

Forward citations

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

Volume 11, issue 4 (2007)