  Extending our results in "Entropy conjecture for continuous maps of
nilmanifolds", to appear in Israel Jour. of Math., we confirm that Entropy
Conjecture holds for every continuous self-map of a compact $K(\pi,1)$ manifold
with the fundamental group $\pi$ torsion free and virtually nilpotent, in
particular for every continuous map of an infra-nilmanifold. In fact we prove a
stronger version, a lower estimate of the topological entropy of a map by
logarithm of the spectral radius of an associated "linearization matrix" with
integer entries.
  From this, referring to known estimates of Mahler measure of polynomials, we
deduce some absolute lower bounds for the entropy.
