Lefschetz fibrations and an invariant of finitely presented groups

Details Lefschetz fibrations and an invariant of finitely presented groups Lefschetz fibrations and an invariant of finitely presented groups

2007-03-07

arxiv.org/abs/math/0703196v1

Mathematics

Geometric Topology

20 pages, 8 figures

Scientific paper

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 $\Gamma$ to be the minimal genus of a Lefschetz fibration with fundamental group $\Gamma$. We also give some estimates of the genus of certain groups.

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