Planar open books, monodromy factorizations and symplectic fillings

Olga Plamenevskaya, Jeremy Van Horn-Morris
2010 Geometry and Topology  
We study fillings of contact structures supported by planar open books by analyzing positive factorizations of their monodromy. Our method is based on Wendl's theorem on symplectic fillings of planar open books. We prove that every virtually overtwisted contact structure on L(p,1) has a unique filling, and describe fillable and non-fillable tight contact structures on certain Seifert fibered spaces.
doi:10.2140/gt.2010.14.2077 fatcat:5dgdpjah5fhrjm7x5erkwguhqu