TY - JOUR
T1 - Fibrations and log-symplectic structures
AU - Cavalcanti, Gil R.
AU - Klaasse, Ralph L.
PY - 2019/9/9
Y1 - 2019/9/9
N2 - Log-symplectic structures are Poisson structures π on X2n for which ∧nπ 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.
AB - Log-symplectic structures are Poisson structures π on X2n for which ∧nπ 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.
UR - http://www.scopus.com/inward/record.url?scp=85073374788&partnerID=8YFLogxK
UR - https://arxiv.org/pdf/1703.03798.pdf
U2 - 10.4310/JSG.2019.v17.n3.a1
DO - 10.4310/JSG.2019.v17.n3.a1
M3 - Article
AN - SCOPUS:85073374788
SN - 1527-5256
VL - 17
SP - 603
EP - 638
JO - Journal of Symplectic Geometry
JF - Journal of Symplectic Geometry
IS - 3
ER -