Fillability of small Seifert fibered spaces

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 characterize fillable structures among zero-twisting contact structures on small Seifert fibered spaces of the form $M(-1;r_1,r_2,r_3)$. The result is obtained by analyzing monodromy factorizations of associated planar open books.