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Fillability of small Seifert fibered spaces
Published online by Cambridge University Press: 25 November 2022
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.
- 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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