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Fillability of small Seifert fibered spaces

Published online by Cambridge University Press:  25 November 2022

IRENA MATKOVIČ
IRENA MATKOVIČ*
Affiliation:
Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden e-mail: irena.matkovic@math.uu.se
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Abstract

On small Seifert fibered spaces $M(e_0;\,r_1,r_2,r_3)$ with $e_0\neq-1,-2,$ all tight contact structures are Stein fillable. This is not the case for $e_0=-1$ or $-2$. However, for negative twisting structures it is expected that they are all symplectically fillable. Here, we characterise fillable structures among zero-twisting contact structures on small Seifert fibered spaces of the form $M\left({-}1;\,r_1,r_2,r_3\right)$. The result is obtained by analysing monodromy factorizations of associated planar open books.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 174 , Issue 3 , May 2023 , pp. 585 - 604
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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