Planar open books, monodromy factorizations and symplectic fillings

Plamenevskaya, Olga¹ ; Van Horn-Morris, Jeremy²

¹ Department of Mathematics, Stony Brook University, Stony Brook NY 11794-3651, USA
² American Institute of Mathematics, Palo Alto CA 94306, USA

Geometry & topology, Tome 14 (2010) no. 4, pp. 2077-2101.

Résumé

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 $L\left(p,1\right)$ has a unique filling, and describe fillable and nonfillable tight contact structures on certain Seifert fibered spaces.

Détail

DOI : 10.2140/gt.2010.14.2077

Keywords: contact structures, open books, symplectic filling

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