We construct Kähler groups with arbitrary finiteness properties by mapping products of closed Riemann surfaces holomorphically onto an elliptic curve: for each r ≥ 3, we obtain large classes of Kähler groups that have classifying spaces with finite (r − 1)-skeleton but do not have classifying spaces with finitely many r-cells. We describe invariants which distinguish many of these groups. Our construction is inspired by examples of Dimca, Papadima and Suciu.Under the additional assumption that all maps f g i are purely branched, we will give the following complete classification of all Kähler groups that can be obtained using our construction.
We give examples of hyperbolic groups which contain subgroups that are of type F 3 but not of type F 4 . These groups are obtained by Dehn filling starting from a non-uniform lattice in PO(8, 1) which was previously studied by Italiano, Martelli and Migliorini.
We construct the first explicit finite presentations for a family of Kähler groups with arbitrary finiteness properties, answering a question of Suciu.
We construct classes of Kähler groups that do not have finite classifying spaces and are not commensurable to subdirect products of surface groups. Each of these groups is the fundamental group of the generic fibre of a holomorphic map from a product of Kodaira fibrations onto an elliptic curve.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.