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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

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SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 27, Issue 3


Legendrian realization in convex Lefschetz fibrations and convex stabilizations

Selman Akbulut / Mehmet F. Arikan
Published Online: 2013-07-05 | DOI: https://doi.org/10.1515/forum-2013-6009


We show that, up to a Liouville homotopy and a deformation of compact convex Lefschetz fibrations on W, any Lagrangian submanifold with trivial first de Rham cohomology group, embedded on a (symplectic) page of the (induced) convex open book on W, can be assumed to be Legendrian in W with the induced contact structure. This can be thought as the extension of Giroux's Legendrian realization (which holds for contact open books) for the case of convex open books. We also show that the convex stabilization of a compact convex Lefschetz fibration on W yields a compact convex Lefschetz fibration on a Liouville domain W' which is exact symplectomorphic to a positive expansion of W. In particular, with the induced structures W and W' are contactomorphic.

Keywords: Liouville; convex symplectic; contact; Lefschetz fibration; Legendrian; open book; stabilization

MSC: 57R65; 58A05; 58D27

About the article

Received: 2013-01-11

Revised: 2013-06-04

Published Online: 2013-07-05

Published in Print: 2015-05-01

Funding Source: NSF FRG

Award identifier / Grant number: DMS-0905917

Funding Source: NSF FRG

Award identifier / Grant number: DMS-1065910

Funding Source: TUBITAK

Award identifier / Grant number: 1109B321200181

Citation Information: Forum Mathematicum, Volume 27, Issue 3, Pages 1829–1847, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2013-6009.

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