Tight contact structures on the Brieskorn spheres -Σ(2,3,6n-1) and contact invariants-Reference-Cited by-同舟云学术

Tight contact structures on the Brieskorn spheres -Σ(2,3,6n-1) and contact invariants

Published:2014-06-11 Issue:718 Volume:2016 Page:1-24
ISSN:1435-5345
Container-title:Journal für die reine und angewandte Mathematik
language:en
Short-container-title:

Author:

Ghiggini Paolo¹,Van Horn-Morris Jeremy²

Affiliation:

1. CNRS , Laboratoire Jean Leray , Université de Nantes , Nantes , France

2. American Institute of Mathematics , Palo Alto , CA , USA

Abstract

Abstract We compute the Ozsváth–Szabó contact invariants for all tight contact structures on the manifolds - Σ ⁢ ( 2 , 3 , 6 ⁢ n - 1 )

{-\Sigma(2,3,6n-1)}

using twisted coefficients and a previous computation by the first author and Ko Honda. This computation completes the classification of the tight contact structures in this family of 3-manifolds.

Funder

Agence Nationale de la Recherche

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2014-0038/pdf

Reference27 articles.

1. M. Dehn, Die Gruppe der Abbildungsklassen, Acta Math. 69 (1938), no. 1, 135–206.

2. J. Etnyre and K. Honda, On the nonexistence of tight contact structures, Ann. of Math. (2) 153 (2001), no. 3, 749–766.

3. P. Ghiggini, Strongly fillable contact 3-manifolds without Stein fillings, Geom. Topol. 9 (2005), 1677–1687.

4. P. Ghiggini, Infinitely many universally tight contact manifolds with trivial Ozsváth–Szabó contact invariants, Geom. Topol. 10 (2006), 335–357.

5. P. Ghiggini, Ozsváth–Szabó invariants and fillability of contact structures, Math. Z. 253 (2006), no. 1, 159–175.

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