Geometry & Topology

Planar open books, monodromy factorizations and symplectic fillings

Olga Plamenevskaya and Jeremy Van Horn-Morris

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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 nonfillable tight contact structures on certain Seifert fibered spaces.

Article information

Geom. Topol., Volume 14, Number 4 (2010), 2077-2101.

Received: 17 December 2009
Accepted: 13 August 2010
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R17: Symplectic and contact topology
Secondary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]

contact structures open books symplectic filling


Plamenevskaya, Olga; Van Horn-Morris, Jeremy. Planar open books, monodromy factorizations and symplectic fillings. Geom. Topol. 14 (2010), no. 4, 2077--2101. doi:10.2140/gt.2010.14.2077.

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