Kodaira fibrations, K\"ahler groups, and finiteness properties
  We construct classes of K\"ahler 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. 
Martin R. Bridson, Claudio Llosa Isenrich
math.GT math.AG math.GR