Each Abelian subgroup of the fundamental group of a compact and locally simply connected -dimensional length space with no conjugate points is isomorphic to for some . 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.
Cite this article
James Dibble, Abelian subgroups of the fundamental group of a space with no conjugate points. Groups Geom. Dyn. 15 (2021), no. 2, pp. 683–690DOI 10.4171/GGD/618