Kaehler groups, quasi-projective groups, and 3-manifold groups

TL;DR

This paper explores the relationship between 3-manifold groups and complex geometric groups, establishing conditions under which these groups imply specific topological structures of the manifolds.

Contribution

It proves new results linking Kaehler and quasi-projective groups to the topology of 3-manifolds, clarifying their geometric and topological implications.

Findings

If N has non-empty, toroidal boundary and (N) is Kaehler, then N is a product of a torus and an interval.

If N has empty or toroidal boundary and (N) is quasi-projective, then all prime components of N are graph manifolds.

Abstract

We prove two results relating 3-manifold groups to fundamental groups occurring in complex geometry. Let N be a compact, connected, orientable 3-manifold. If N has non-empty, toroidal boundary, and \pi_1(N) is a Kaehler group, then N is the product of a torus with an interval. On the other hand, if N has either empty or toroidal boundary, and \pi_1(N) is a quasi-projective group, then all the prime components of N are graph manifolds.