## Geometry & Topology

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

#### Abstract

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

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

Dates
Accepted: 13 August 2010
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513883514

Digital Object Identifier
doi:10.2140/gt.2010.14.2077

Mathematical Reviews number (MathSciNet)
MR2740642

Zentralblatt MATH identifier
1319.57019

#### Citation

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. https://projecteuclid.org/euclid.gt/1513883514

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