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The
topology of Stein fillable manifolds in high dimensions,
II
Jonathan Bowden, Diarmuid Crowley and András I StipsiczAppendix: Bernd C Kellner |
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Geometry & Topology 19 (2015) 2995–3030
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Abstract |
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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 . 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 that there are almost contact structures on the –sphere which are not Stein fillable. This implies the same result for all highly connected –manifolds which admit almost contact structures. The proofs rely on a new number-theoretic result about Bernoulli numbers. |
Keywords
Stein fillability, surgery, contact structures, bordism
theory
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Mathematical Subject Classification 2010
Primary: 32E10
Secondary: 57R17, 57R65
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References |
Publication
Received: 28 October 2014
Revised: 23 February 2015
Accepted: 28 March 2015
Published: 20 October 2015
Proposed: Yasha Eliashberg
Seconded: Peter Teichner, Simon Donaldson
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Authors |
| Jonathan Bowden | |
| Ludwig-Maximillians
Universität Mathemathisches Institut Theresienstr. 39 D-80333 Munich Germany |
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| Diarmuid Crowley | |
| Institute of Mathematics University of Aberdeen Aberdeen AB24 3UE UK |
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| András I Stipsicz | |
| Rényi Institute of Mathematics Hungarian Academy of Sciences Réaltanoda utca 13-15 Budapest, H-1053 Hungary |
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| Bernd C Kellner | |
| Universität Göttingen Mathematisches Institut D-37073 Göttingen Germany |
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