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Kodaira fibrations, Kähler groups, and finiteness properties. (English) Zbl 1432.32020

Recall that a Kähler group is a group that can be realised as the fundamental group of a compact Kähler manifold. The aim of this paper is to present a new technique for constructing Kähler groups. The authors construct classes of Kähler groups that do not have finite classifying spaces and are not commensurable to subdirect products of surface groups. By applying this technique to Kodaira fibrations, they obtain Kähler groups that do not have finite classifying spaces. 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. They also develop a criterion for deciding when these groups are commensurable with residually free groups.

MSC:

32J27 Compact Kähler manifolds: generalizations, classification
20J05 Homological methods in group theory
32Q15 Kähler manifolds
20F65 Geometric group theory
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