Geometry & Topology

The topology of Stein fillable manifolds in high dimensions, II

Jonathan Bowden, Diarmuid Crowley, and András I Stipsicz

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Abstract

We continue our study of contact structures on manifolds of dimension at least five using surgery-theoretic methods. Particular applications include the existence of “maximal” almost contact manifolds with respect to the Stein cobordism relation as well as the existence of weakly fillable contact structures on the product M × S2. We also study the connection between Stein fillability and connected sums: we give examples of almost contact manifolds for which the connected sum is Stein fillable, while the components are not.

Concerning obstructions to Stein fillability, we show for all k > 1 that there are almost contact structures on the (8k1)–sphere which are not Stein fillable. This implies the same result for all highly connected (8k1)–manifolds which admit almost contact structures. The proofs rely on a new number-theoretic result about Bernoulli numbers.

Article information

Source
Geom. Topol., Volume 19, Number 5 (2015), 2995-3030.

Dates
Received: 28 October 2014
Revised: 23 February 2015
Accepted: 28 March 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1510858855

Digital Object Identifier
doi:10.2140/gt.2015.19.2995

Mathematical Reviews number (MathSciNet)
MR3416120

Zentralblatt MATH identifier
1380.32016

Subjects
Primary: 32E10: Stein spaces, Stein manifolds
Secondary: 57R17: Symplectic and contact topology 57R65: Surgery and handlebodies

Keywords
Stein fillability surgery contact structures bordism theory

Citation

Bowden, Jonathan; Crowley, Diarmuid; Stipsicz, András I. The topology of Stein fillable manifolds in high dimensions, II. Geom. Topol. 19 (2015), no. 5, 2995--3030. doi:10.2140/gt.2015.19.2995. https://projecteuclid.org/euclid.gt/1510858855


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