Fillability of small Seifert fibered spaces

Abstract

AbstractOn 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.