Family of Jacobian manifolds and characteristic classes of surface bundles
In our previous papers [see, e.g., Bull. Am. Math. Soc. 11, New Ser., 386-388 (1984); ''Characteristic classes of surface bundles, I'' (preprint); II (in preparation); ''Characteristic classes of \(T^ 2\)- bundles (preprint)], we have defined characteristic classes for surface bundles, namely differentiable fibre bundles whose fibres are closed orientable surfaces, and investigated general properties of them. The purpose of the present note is to announce new results concerning them. More precisely we study cohomological properties of the natural map from a given surface bundle to its associated ''family of Jacobian manifolds'' and by using them, we derive a rather strong linear dependence relations among our characteristic classes.
characteristic classes for surface bundles
scientific article; zbMATH DE number 3915246