Symplectic fillability of tight contact structures on torus bundles
type: Item
instance of: scholarly article
title: Symplectic fillability of tight contact structures on torus bundles
zbMATH Open document ID: 0974.53061
author: Fan Ding
author: Hansjörg Geiges
published in: Algebraic \& Geometric Topology
publication date: 2001-03-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0104109
full work available at URL: https://eudml.org/doc/121419
full work available at URL: agt-1-8.abs.html
review text: A manifold \(M\) with contact structure \(\xi\) is weakly symplectically fillable if \(M = \partial W\), where \((W, \omega)\) is a symplectic manifold such that \(\omega|_\xi\) is nondegenerate (and orientations are compatible). \(M\) is stongly symplectically fillable if \(M = \partial W\), \((W, \omega)\) symplectic, and there is a Liouville vector field \(X\) (outward on \(\partial W\)) with \(\xi = \text{ker}(i_X\omega|_M)\). Work of Giroux and Eliashberg describes when tight contact structures on \(T^3\) are weakly or strongly symplectically fillable. In this paper, the same type of description is given for \(T^2\)-bundles over \(S^1\) constructed from elements of \(\text{SL}_2(\mathbb Z)\) with certain associated tight contact structures \(\xi_n\).
reviewed by: John Oprea
Mathematics Subject Classification ID: 53D35
Mathematics Subject Classification ID: 57R17
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 57R65
zbMATH DE Number: 1580599
zbMATH Keywords: tight contact structure
zbMATH Keywords: weak symplectic filling
zbMATH Keywords: contact surgery
zbMATH Keywords: strong symplectic filling
MaRDI profile type: Publication
OpenAlex ID: W2042522101
arXiv ID: math/0104109
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DOI: 10.2140/AGT.2001.1.153
description: scientific article; zbMATH DE number 1580599