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

Diarmuid J. CrowleyPeter 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...

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