Journal of Symplectic Geometry

Volume 17 (2019)

Number 3

Fibrations and log-symplectic structures

Pages: 603 – 638

DOI: https://dx.doi.org/10.4310/JSG.2019.v17.n3.a1

Authors

Gil R. Cavalcanti (Department of Mathematics, Utrecht University, Utrecht, The Netherlands)

Ralph L. Klaasse (Department of Mathematics, Utrecht University, Utrecht, The Netherlands; and Département de Mathématique, Université libre de Bruxelles, Belgium)

Abstract

Log-symplectic structures are Poisson structures $\pi$ on $X^{2n}$ for which $\wedge^n \pi$ vanishes transversally. By viewing them as symplectic forms in a Lie algebroid, the $b$-tangent bundle, we use symplectic techniques to obtain existence results for $\log$-symplectic structures on total spaces of fibration-like maps. More precisely, we introduce the notion of a $b$-hyperfibration and show that they give rise to logsymplectic structures. Moreover, we link $\log$-symplectic structures to achiral Lefschetz fibrations and folded-symplectic structures.

This research was supported by VIDI grant number 639.032.221 from NWO, the Netherlands Organisation for Scientific Research.

Received 3 June 2016

Accepted 9 November 2017

Published 9 September 2019