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On the groups Θ n F of a sphere

S. Dragotti, G. Magro, L. Parlato (2000)

Bollettino dell'Unione Matematica Italiana

In questo articolo studiamo i gruppi Θ h F di una sfera S n e proviamo che il gruppo Θ n F S n , x 0 è isomorfo all'ennesimo gruppo di omotopia di S n , x 0 , nell'ipotesi che F sia una classe coconnessa di links ammissibili.

On the non-invariance of span and immersion co-dimension for manifolds

Diarmuid J. Crowley, Peter D. Zvengrowski (2008)

Archivum Mathematicum

In this note we give examples in every dimension m 9 of piecewise linearly homeomorphic, closed, connected, smooth m -manifolds which admit two smoothness structures with differing spans, stable spans, and immersion co-dimensions. In dimension 15 the examples include the total spaces of certain 7 -sphere bundles over S 8 . The construction of such manifolds is based on the topological variance of the second Pontrjagin class: a fact which goes back to Milnor and which was used by Roitberg to give examples...

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 .

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