Exotic Stein fillings with arbitrary fundamental group

Anar Akhmedov, Burak Ozbagci

Published 2012-12-08, updated 2013-12-01Version 2

For any finitely presentable group $G$, we show the existence of an isolated complex surface singularity link which admits infinitely many exotic Stein fillings such that the fundamental group of each filling is isomorphic to $G$. We also provide an infinite family of closed exotic smooth four-manifolds with the fundamental group $G$ such that each member of the family admits a non-holomorphic Lefschetz fibration over the two-sphere.