Abelian subgroups of the fundamental group of a space with no conjugate points (Q2245024)

Summary: Each abelian subgroup of the fundamental group of a compact and locally simply connected \(d\)-dimensional length space with no conjugate points is isomorphic to \(\mathbb{Z}^k\) for some \(0 \leq k \leq d\). It follows from this and previously known results that each solvable subgroup of the fundamental group is a Bieberbach group. In the Riemannian setting, this may be proved using a novel property of the asymptotic norm of each abelian subgroup.