Surgery diagrams for horizontal contact structures
type: Item
instance of: scholarly article
title: Surgery diagrams for horizontal contact structures
title: A NOTE ON CONTACT SURGERY DIAGRAMS
zbMATH Open document ID: 1174.57001
zbMATH Open document ID: 1068.57026
DOI: 10.1142/S0129167X05002746
DOI: 10.1007/S10474-007-7132-0
published in: Acta Mathematica Hungarica
published in: International Journal of Mathematics
publication date: 2008-10-21T00:00:00Z
publication date: 2005-03-18T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0610104
review text: The author considers horizontal contact structures on non-positive plumbing trees of oriented circle bundles over spheres with negative Euler numbers. Here, a contact structure on such a manifold is said to be horizontal if the contact planes (oriented by the differential of the contact form) are positively transverse to the fibers of the bundles involved in the plumbing, and the plumbing tree is said to be non-positive if for every vertex of the tree the sum of the degree of the vertex and the Euler number of the bundle corresponding to that vertex is non-positive. The author's aim in this paper is to give a new description of such contact stuctures up to isomorphism, by describing Legendrian surgery diagrams for these structures. The author gives an application to the study of Milnor fillable contact 3-manifolds, that is, contact 3-manifolds isomorphic to the contact boundary of an isolated complex surface singularity. By a result of \textit{C. Caubel, A. Némethi} and \textit{P. Popescu-Pampu} [Topology 45, No.~3, 637--689 (2006; Zbl 1098.53064)] any 3-manifold admits, up to isomorphism, at most one Milnor fillable contact structure. As an application of his constructions, the author obtains a description of the Milnor fillable contact structures of some Milnor fillable 3-manifolds.
reviewed by: Athanase Papadopoulos
Mathematics Subject Classification ID: 57R17
Mathematics Subject Classification ID: 57R65
Mathematics Subject Classification ID: 57M99
zbMATH DE Number: 5355156
zbMATH DE Number: 2147034
zbMATH Keywords: contact structures
zbMATH Keywords: surgery diagrams
zbMATH Keywords: open book decompositions
zbMATH Keywords: Milnor fillable
zbMATH Keywords: contact manifold
zbMATH Keywords: surgery
zbMATH Keywords: open book decomposition
author: Burak Ozbagci
MaRDI profile type: Publication
OpenAlex ID: W2158402308
arXiv ID: math/0610104
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description: scientific article; zbMATH DE number 2147034
alternative label: A NOTE ON CONTACT SURGERY DIAGRAMS