Branched covers of elliptic curves and Kähler groups with exotic finiteness properties

Abstract

We construct Kähler groups with arbitrary finiteness properties by mapping products of closed Riemann surfaces holomorphically onto an elliptic curve: for each $r\ge 3$, 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.

22 pages, 3 figures, V3: Minor corrections and improvements to the exposition. Final accepted version, to appear in the Annales de l'Institut Fourier

References in corpus (4)

• On the finite presentation of subdirect products and the nature of residually free groups
• Non-finiteness properties of fundamental groups of smooth projective varieties
• Quasi-Kähler Bestvina-Brady groups
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Cited by in corpus (1)

• Finite presentations for Kähler groups with arbitrary finiteness properties