Kähler groups from maps onto higher dimensional tori

Claudio Llosa Isenrich

Published 2017-01-04Version 1

Following the work of Delzant and Gromov, there is great interest in understanding which subgroups of direct products of surface groups are K\"ahler. We construct new classes of examples. These arise as kernels of a homomorphisms from direct products of surface groups onto free abelian groups of even rank. They have exotic finiteness properties: For any $r\geq 2$ our class of examples contains K\"ahler groups that have a classifying space with finite $r$-skeleton while not having a classifying space with finitely many $s$-cells for some $s>r$. The gap between $s$ and $r$ begs intriguing questions.