Planar open books, monodromy factorizations, and symplectic fillings

Details Planar open books, monodromy factorizations, and symplectic fillings Planar open books, monodromy factorizations, and symplectic fillings

2009-12-10

arxiv.org/abs/0912.1916v1

Mathematics

Geometric Topology

20 pages, 13 figures

Scientific paper

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.

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