Lefschetz fibrations and an invariant of finitely presented groups

Mustafa Korkmaz

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arXiv · math/0703196

Lefschetz fibrations and an invariant of finitely presented groups

Mustafa Korkmaz

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Abstract

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.

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BibTeX RIS

Mustafa Korkmaz. 2007-03-07. Lefschetz fibrations and an invariant of finitely presented groups. https://arxiv.org/abs/math/0703196

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