Volume 20, issue 1 (2020)

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Tight small Seifert fibered manifolds with $e_0=-2$

Bülent Tosun

Algebraic & Geometric Topology 20 (2020) 1–27

We provide the classification of tight contact structures on some small Seifert fibered manifolds. As an application of this classification, combined with work of Lekili, we obtain infinitely many counterexamples to a question of Honda, Kazez and Matić that asks whether a right-veering, nondestabilizable open book necessarily supports a tight contact structure.

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small Seifert fibered spaces, tight contact structures, classification of tight structures
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 53D10
Received: 3 January 2017
Revised: 27 September 2018
Accepted: 24 October 2018
Published: 23 February 2020
Bülent Tosun
Department of Mathematics
University of Alabama
Tuscaloosa, AL
United States