Geodesic
Low-dimensional solenoidal manifolds
Alberto Verjovsky1
1Universidad Nacional Autónoma de México, Cuernavaca, Morelos, Mexico
EMS surveys in mathematical sciences, Volume 10 (2023) no. 1, pp. 131-178

See the original article notice from the EMS Press source

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.
DOI: 10.4171/emss/69
Classification: 57-XX, 32-XX
Keywords: solenoidal manifolds, laminations, profinite completions

Alberto Verjovsky  1

1 Universidad Nacional Autónoma de México, Cuernavaca, Morelos, Mexico 
Alberto Verjovsky. Low-dimensional solenoidal manifolds. EMS surveys in mathematical sciences, Volume 10 (2023) no. 1, pp. 131-178. doi: 10.4171/emss/69
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