caa a22 4500 386386005 CHVBK 20180307112058.0 cr unu---uuuuu 161130e198901 xx s 000 0 eng 10.1017/S0305004100001389 doi S0305004100001389 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100001389 Morita Shigeyuki Department of Mathematics, Faculty of Science, Tokyo Institute of Technology, Japan Families of Jacobian manifolds and characteristic classes of surface bundles. II [Elektronische Daten] [Shigeyuki Morita] Let Σg be a closed orientable surface of genus g, which will be assumed to be greater than one throughout this paper. In our previous paper [11], we have associated to any oriented ∑g-bundle π: E → X with a cross-section s: X → E a flat T2g-bundle π: J → X and a fibre-preserving embedding j: E → J such that the restriction of j to any fibre Ep = π−1(p)(p X) is equivalent to the Jacobi mapping of Ep with respect to some conformal structure on it and relative to the base-point s(p) Ep. There is a canonical oriented S1-bundle over J and the main result of [11] is the identification of the Euler class of the pullback of this S1-bundle by the map j as an element of H2(E, ). In this paper we deal with the case of Σg-bundles without cross-sections. First of all we associate a flat T2g-bundle π′: J′ → X to any oriented Σg-bundle π: E → X and construct a fibre-preserving embedding j′: E → J′ such that the restriction of j′ to any fibre Ep is equivalent to some translation of the Jacobi mapping of it. Although our original motivation for the present work came from a different source, this should be considered as a topological version of Earle's embedding theorem [5] which states that any holomorphic family of compact Riemann surfaces over a complex manifold can be embedded in a certain associated family of the corresponding Jacobian varieties in an essentially unique way. Copyright © Cambridge Philosophical Society 1989 Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 79-101 0305-0041 105:1<79 1989 105 PSP https://doi.org/10.1017/S0305004100001389 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100001389 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Morita Shigeyuki Department of Mathematics, Faculty of Science, Tokyo Institute of Technology, Japan NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 79-101 0305-0041 105:1<79 1989 105 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge