Kaehler groups and duality

TL;DR

This paper investigates the topological properties of Kaehler groups, demonstrating that certain duality groups with high dimension cannot be fundamental groups of compact Kaehler manifolds due to Betti number constraints.

Contribution

It establishes new restrictions on Kaehler groups by linking duality properties and Betti numbers, especially for high-dimensional cases.

Findings

High-dimensional duality groups have non-zero second or fourth Betti number if they are Kaehler.

Cocompact p-adic lattices of rank > 6 are not Kaehler.

Provides topological criteria for identifying non-Kaehler groups.

Abstract

This is the topological part of two papers on the cohomology of Kaehler groups. In this paper we show that if a linear duality group of dimension larger than 6 is the fundamental group of a compact Kaehler manifold then its second or its fourth Betti number is non-zero. As a corollary a cocompact p-adic lattice of rank larger than 6 is never Kaehler.