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Pro-groups and generalizations of a theorem of Bing

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 نشر من قبل Steven Hurder
 تاريخ النشر 2018
  مجال البحث
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A matchbox manifold is a generalized lamination, which is a continuum whose path components define the leaves of a foliation of the space. A matchbox manifold is M-like if it has the shape of a fixed topological space M. When M is a closed manifold, in a previous work, the authors have shown that if $frak M$ is a matchbox manifold which is M-like, then it is homeomorphic to a weak solenoid. In this work, we associate to a weak solenoid a pro-group, whose pro-isomorphism class is an invariant of the homeomorphism class of $frak M$. We then show that an M-like matchbox manifold is homeomorphic to a weak solenoid whose base manifold has fundamental group which is non co-Hopfian; that is, it admits a non-trivial self-embedding of finite index. We include a collection of examples illustrating this conclusion.



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