%0 Journal Article
%T Lefschetz pencils and finitely presented groups
%A Ryoma Kobayashi
%A Naoyuki Monden
%J Mathematics
%D 2014
%I arXiv
%X 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 $\Gamma$.
%U http://arxiv.org/abs/1404.5380v1