A new class of homology and cohomology 3-manifolds

Abstract

We show that for any set of primes $\mathcal{P}$ there exists a space $M_{\mathcal{P}}$ which is a homology and cohomology 3-manifold with coefficients in ${\mathbb{Z}}_p$ for $p\in \mathcal{P}$ and is not a homology or cohomology 3-manifold with coefficients in ${\mathbb{Z}}_q$ for $q\notin \mathcal{P}$. Moreover, $M_{\mathcal{P}}$ is neither a homology nor cohomology 3-manifold with coefficients in $\mathbb{Z}$ or $\mathbb{Q}$.