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arXiv · 1606.00156

Fibrations and log-symplectic structures

Gil R. Cavalcanti·Ralph L. Klaasse
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Abstract

Log-symplectic structures are Poisson structures $\pi$ on $X^{2n}$ for which $\bigwedge^n \pi$ 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 log-symplectic structures. Moreover, we link log-symplectic structures to achiral Lefschetz fibrations and folded-symplectic structures.

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BibTeXRIS

Gil R. Cavalcanti, Ralph L. Klaasse. 2016-06-01. Fibrations and log-symplectic structures. https://doi.org/10.4310/jsg.2019.v17.n3.a1

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