Planar open books, monodromy factorizations and symplectic fillings

Plamenevskaya, Olga; Van Horn-Morris, Jeremy

doi:10.2140/gt.2010.14.2077

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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 2000

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

Volume 14, issue 4 (2010)