Commutators, Lefschetz fibrations and the signatures of surface bundles

Abstract

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.

20 pages, 7 figures, accepted for publication in Topology

References in corpus (1)

• An elementary approach to the mapping class group of a surface

Cited by in corpus (7)

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• Remarks on codes from modular curves: MAGMA applications
• Upper bounds for the minimal number of singular fibers in a Lefschetz fibration over the torus
• Signatures of surface bundles and stable commutator lengths of Dehn twists
• A note on the fundamental group of Kodaira fibrations
• Extra-special quotients of surface braid groups and double Kodaira fibrations with small signature
• Surface bundles over surfaces: new inequalities between signature, simplicial volume and Euler characteristic