#### Volume 18, issue 1 (2018)

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

### Irena Matkovič

Algebraic & Geometric Topology 18 (2018) 111–152
##### 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 $M\left(-1;{r}_{1},{r}_{2},{r}_{3}\right)$) 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
Primary: 57R17