### Universal manifold pairings and positivity.

Freedman, Michael H., Kitaev, Alexei, Nayak, Chetan, Slingerland, Johannes K., Walker, Kevin, Wang, Zhenghan (2005)

Geometry & Topology

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Freedman, Michael H., Kitaev, Alexei, Nayak, Chetan, Slingerland, Johannes K., Walker, Kevin, Wang, Zhenghan (2005)

Geometry & Topology

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Kreck, Matthias (2001)

Geometry & Topology

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Lisca, Paolo, Stipsicz, Andras I. (2003)

Geometry & Topology

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Nicholaas H. Kuiper (1967)

Publications Mathématiques de l'IHÉS

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Alberto Tognoli (2003)

Bollettino dell'Unione Matematica Italiana

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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.

Yusuf Kaya (2012)

Rendiconti del Seminario Matematico della Università di Padova

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Hatcher, Allen, McCullough, Darryl (1997)

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

Archivum Mathematicum

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

Okun, Boris (2002)

Algebraic & Geometric Topology

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Kühnel, Wolfgang (2004)

Documenta Mathematica

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