Displaying similar documents to “An invariant of smooth 4-manifolds.”

Topological manifolds and real algebraic geometry

Alberto Tognoli (2003)

Bollettino dell'Unione Matematica Italiana


We study the problem of approximating, up to homotopy, compact topological manifolds by real algebraic varieties. As a consequence, we realize any integral non-degenerate quadratic form as the intersection form of a real algebraic variety. This is related to a well-known result, due to Freedman [F], on the topology of closed simply-connected topological 4 -manifolds.

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...