Exotic smooth structures on nonpositively curved symmetric spaces.

Okun, Boris

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An invariant of smooth 4-manifolds.

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Nonzero degree tangential maps between dual symmetric spaces.

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h-cobordisms between 1-connected 4-manifolds.

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Topological manifolds and real algebraic geometry

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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.

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Framed bicobordism

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

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

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In this note we give examples in every dimension $m \geq 9$ 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...