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Planar open books, monodromy factorizations and symplectic fillings

Olga Plamenevskaya and Jeremy Van Horn-Morris

Geometry & Topology 14 (2010) 2077–2101

DOI: 10.2140/gt.2010.14.2077

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.

Keywords

contact structures, open books, symplectic filling

Mathematical Subject Classification

Primary: 57R17

Secondary: 53D35

References
Publication

Received: 17 December 2009
Accepted: 13 August 2010
Published: 16 September 2010
Proposed: Yasha Eliashberg
Seconded: Peter Ozsvath, Leonid Polterovich

Authors
Olga Plamenevskaya
Department of Mathematics
Stony Brook University
Stony Brook NY 11794-3651
USA
Jeremy Van Horn-Morris
American Institute of Mathematics
Palo Alto CA 94306
USA