The homotopy type of certain laminated manifolds

Daverman, R. J.; Tinsley, F. C.

doi:10.1090/S0002-9939-1986-0826506-1

The homotopy type of certain laminated manifolds
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by R. J. Daverman and F. C. Tinsley PDF

Proc. Amer. Math. Soc. 96 (1986), 703-708 Request permission

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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Homological group theory