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The homotopy type of certain laminated manifolds

Authors: R. J. Daverman and F. C. Tinsley
Journal: Proc. Amer. Math. Soc. 96 (1986), 703-708
MSC: Primary 57N15; Secondary 55P15
MathSciNet review: 826506
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Abstract: Let $ M$ denote a connected $ (n + 1)$-manifold $ n \geqslant 5$. A lamination $ G$ of $ M$ is an use decomposition of $ M$ into closed connected $ n$-manifolds. Daverman has shown that the decomposition space $ M/G$ is homeomorphic to a $ 1$-manifold possibly with boundary. If $ M/G = {R^1}$, we prove that $ M$ has the homotopy type of an $ n$-manifold if and only if $ {\prod _1}(M)$ is finitely presented. In the case that $ M/G = {S^1}$ we use the above result to construct an approximate fibration $ f:M \to {S^1}$. We then discuss the important interactions of this study with that of perfect subgroups of finitely presented groups.

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Keywords: Lamination, decomposition, approximate fibration, homotopy type, finitely presented group, perfect subgroup
Article copyright: © Copyright 1986 American Mathematical Society