Lefschetz pencils and finitely presented groups

Abstract

In this paper, given a finitely presented group $\Gamma$, we provide the explicit monodromy of a Lefschetz fibration with $(-1)$-sections whose total space has fundamental group $\Gamma$ by applying "twisted substitutions" to that of the Lefschetz fibration constructed by Cadavid and independently Korkmaz. Consequently, we obtain an upper bound for the minimum $g$ such that there exists a genus-$g$ Lefschetz pencil on a smooth 4-manifold whose fundamental group is isomorphic to $\Gamma$.

25 pages, 10 figures

References in corpus (4)

• Positive Dehn Twist Expressions for some New Involutions in the Mapping Class Group II
• The canonical pencils on Horikawa surfaces
• On genera of Lefschetz fibrations and finitely presented groups
• Positive Dehn Twist Expressions for some New Involutions in Mapping Class Group

Cited by in corpus (1)

• Non-holomorphic Lefschetz fibrations with $(-1)$-sections