Commutators, Lefschetz fibrations and the signatures of surface bundles

Details Commutators, Lefschetz fibrations and the signatures of surface bundles Commutators, Lefschetz fibrations and the signatures of surface bundles

2001-03-27

arxiv.org/abs/math/0103176v1

Topology 41 (2002), 961--977

Mathematics

Geometric Topology

20 pages, 7 figures, accepted for publication in Topology

Scientific paper

10.1016/S0040-9383(01)00011-8

We construct examples of Lefschetz fibrations with prescribed singular fibers. By taking differences of pairs of such fibrations with the same singular fibers, we obtain new examples of surface bundles over surfaces with non-zero signature. From these we derive new upper bounds for the minimal genus of a surface representing a given element in the second homology of a mapping class group.

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