On the non-invariance of span and immersion co-dimension for manifolds
In this note we give examples in every dimension of piecewise linearly homeomorphic, closed, connected, smooth -manifolds which admit two smoothness structures with differing spans, stable spans, and immersion co-dimensions. In dimension the examples include the total spaces of certain -sphere bundles over . 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...