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On the topological structure of compact 5-manifolds

Alberto Cavicchioli, Fulvia Spaggiari (1993)

Commentationes Mathematicae Universitatis Carolinae

We classify the genus one compact (PL) 5-manifolds and prove some results about closed 5-manifolds with free fundamental group. In particular, let M be a closed connected orientable smooth 5 -manifold with free fundamental group. Then we prove that the number of distinct smooth 5 -manifolds homotopy equivalent to M equals the 2 -nd Betti number (mod 2 ) of M .

Products of open manifolds with ℝ

Craig R. Guilbault (2007)

Fundamenta Mathematicae

We present a characterization of those open n-manifolds (n ≥ 5) whose products with the real line are homeomorphic to interiors of compact (n+1)-manifolds with boundary.

Properly homotopic nontrivial planes are isotopic

Bobby Winters (1995)

Fundamenta Mathematicae

It is proved that two planes that are properly homotopic in a noncompact, orientable, irreducible 3-manifold that is not homeomorphic to 3 are isotopic. The end-reduction techniques of E. M. Brown and C. D. Feustal and M. G. Brin and T. L. Thickstun are used.

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