%0 Journal Article %T Isometry-invariant geodesics and the fundamental group, II %A Leonardo Macarini %A Marco Mazzucchelli %J Mathematics %D 2015 %I arXiv %X We show that on a closed Riemannian manifold with fundamental group isomorphic to $\mathbb{Z}$, other than the circle, every isometry that is homotopic to the identity possesses infinitely many invariant geodesics. This completes a recent result of the second author. %U http://arxiv.org/abs/1504.05685v1