On the Euler number of quasiregularly elliptic manifolds

A compact [Formula: see text]-dimensional Riemannian manifold [Formula: see text] is a quasiregularly elliptic manifold if it admits a nonconstant quasiregular map [Formula: see text]. In this paper, we show that the Euler number of a compact quasiregularly elliptic manifold with infinite fundamental group is zero. We also discuss Morse–Novikov cohomology groups of quasiregularly elliptic manifolds.