Classification of tight contact structures on small Seifert fibered L–spaces

Matkovič, Irena

doi:10.2140/agt.2018.18.111

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Classification of tight contact structures on small Seifert fibered $L$–spaces

Irena Matkovič

Algebraic & Geometric Topology 18 (2018) 111–152

DOI: 10.2140/agt.2018.18.111

Abstract

We identify tight contact structures on small Seifert fibered $L$ –spaces as exactly the structures having nonvanishing contact invariant, and classify them by their induced ${Spin}^{c}$ structures. The result (in the new case of $M (- 1; r_{1}, r_{2}, r_{3})$ ) is based on the translation between convex surface theory and the tightness criterion of Lisca and Stipsicz.

Keywords

Seifert fibered $3$–manifolds, tight contact structures, contact Ozsváth–Szabó invariant, convex surface theory

Mathematical Subject Classification 2010

Primary: 57R17

References

Publication

Received: 29 January 2016

Revised: 30 March 2017

Accepted: 3 July 2017

Published: 10 January 2018

Authors

Irena Matkovič
Department of Mathematics Central European University Budapest Hungary

Volume 18, issue 1 (2018)