Lefschetz fibrations and an invariant of finitely presented groups

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Every finitely presented group is the fundamental group of the total space of a Lefschetz fibration. This follows from results of Gompf and Donaldson, and was also proved by Amoros-Bogomolov-Katzarkov-Pantev. We give another proof by providing the monodromy explicitly. We then define the genus of a finitely presented group $Γ$ to be the minimal genus of a Lefschetz fibration with fundamental group $Γ$. We also give some estimates of the genus of certain groups.
20 pages, 8 figures

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Geometric Topology

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http://salesiana.dossiersoluciones.com/handle/123456789/125237

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0703196
 http://arxiv.org/abs/math/0703196

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arXiv