Abelian subgroups of the fundamental group of a space with no conjugate points
Groups, geometry, and dynamics, Tome 15 (2021) no. 2, pp. 683-690
Voir la notice de l'article provenant de la source EMS Press
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 Zk for some 0≤k≤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.
Classification :
20-XX, 53-XX
Mots-clés : No conjugate points, Abelian subgroup, solvable subgroup, Busemann function, asymptotic norm
Mots-clés : No conjugate points, Abelian subgroup, solvable subgroup, Busemann function, asymptotic norm
Affiliations des auteurs :
James Dibble 1
James Dibble. Abelian subgroups of the fundamental group of a space with no conjugate points. Groups, geometry, and dynamics, Tome 15 (2021) no. 2, pp. 683-690. doi: 10.4171/ggd/618
@article{10_4171_ggd_618,
author = {James Dibble},
title = {Abelian subgroups of the fundamental group of a space with no conjugate points},
journal = {Groups, geometry, and dynamics},
pages = {683--690},
year = {2021},
volume = {15},
number = {2},
doi = {10.4171/ggd/618},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/618/}
}
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