Journal article

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

Diarmuid Crowley, Peter Zvengrowski

Archivum Mathematicum | Masarykova Universita | Published : 2008

#### Abstract

In this note we give examples in every dimension &#36;m \ge 9&#36; of piecewise linearly homeomorphic, closed, connected, smooth &#36;m&#36;-manifolds which admit two smoothness structures with differing spans, stable spans, and immersion co-dimensions. In dimension &#36;15&#36; the examples include the total spaces of certain &#36;7&#36;-sphere bundles over &#36;S^8&#36;. 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 of span variation in dimensions &#36;m \ge 18&#36;. We also show that span does not vary for piecewise linearly homeomorphic smooth manifol..

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