Low-dimensional solenoidal manifolds
EMS surveys in mathematical sciences, Tome 10 (2023) no. 1, pp. 131-178
Voir la notice de l'article provenant de la source EMS Press
In this paper we survey n-dimensional solenoidal manifolds for n=1,2 and 3, and present new results about them. Solenoidal manifolds of dimension n are metric spaces locally modeled on the product of a Cantor set and an open n-dimensional disk. Therefore, they can be “laminated” (or “foliated”) by n-dimensional leaves. By a theorem of A. Clark and S. Hurder, topologically homogeneous, compact solenoidal manifolds are McCord solenoids, i.e., are obtained as the inverse limit of an increasing tower of finite, regular covering spaces of a compact manifold with an infinite and residually finite fundamental group. In this case, their structure is very rich since they are principal Cantor-group bundles over a compact manifold and behave like “laminated” versions of compact manifolds, thus they share many of their properties.
Classification :
57-XX, 32-XX
Mots-clés : solenoidal manifolds, laminations, profinite completions
Mots-clés : solenoidal manifolds, laminations, profinite completions
Affiliations des auteurs :
Alberto Verjovsky 1
Alberto Verjovsky. Low-dimensional solenoidal manifolds. EMS surveys in mathematical sciences, Tome 10 (2023) no. 1, pp. 131-178. doi: 10.4171/emss/69
@article{10_4171_emss_69,
author = {Alberto Verjovsky},
title = {Low-dimensional solenoidal manifolds},
journal = {EMS surveys in mathematical sciences},
pages = {131--178},
year = {2023},
volume = {10},
number = {1},
doi = {10.4171/emss/69},
url = {http://geodesic.mathdoc.fr/articles/10.4171/emss/69/}
}
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