Rational manifold models for duality groups

Abstract

We show that a finite type duality group of dimension $d>2$ is the fundamental group of a $(d+3)$-manifold with rationally acyclic universal cover. We use this to find closed manifolds with rationally acyclic universal cover and some nonvanishing $L^2$-Betti numbers outside the middle dimension, which contradicts a rational analogue of a conjecture of Singer.

25 pages

References in corpus (1)

• Smith theory, L2 cohomology, isometries of locally symmetric manifolds and moduli spaces of curves

Cited by in corpus (1)

• Survey on L^2-invariants and 3-manifolds