141 research outputs found
Three-manifolds and Kaehler groups
We give a simple proof of a result originally due to Dimca and Suciu: a group
that is both Kaehler and the fundamental group of a closed three-manifold is
finite. We also prove that a group that is both the fundamental group of a
closed three-manifold and of a non-Kaehler compact complex surface is infinite
cyclic or the direct product of an infinite cyclic group and a group of order
two.Comment: 6 pages; corrected statement of Theorem 6; final version to appear in
Ann. Inst. Fourie
On products of harmonic forms
We prove that manifolds admitting a Riemannian metric for which products of
harmonic forms are harmonic satisfy strong topological restrictions, some of
which are akin to properties of flat manifolds. Others are more subtle, and are
related to symplectic geometry and Seiberg-Witten theory.
We also prove that a manifold admits a metric with harmonic forms whose
product is not harmonic if and only if it is not a rational homology sphere.Comment: Revised to include flatness of formal metrics on tori of arbitrary
dimensio
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