Kervaire manifold

In mathematics, specifically in differential topology, a Kervaire manifold [math]\displaystyle{ K^{4n+2} }[/math] is a piecewise-linear manifold of dimension [math]\displaystyle{ 4n+2 }[/math] constructed by Michel Kervaire (1960) by plumbing together the tangent bundles of two [math]\displaystyle{ (2n+1) }[/math]-spheres, and then gluing a ball to the result. In 10 dimensions this gives a piecewise-linear manifold with no smooth structure.

See also

• Exotic sphere

References

• Kervaire, Michel (1960), "A manifold which does not admit any differentiable structure", Commentarii Mathematici Helvetici 34: 257–270, doi:10.1007/BF02565940 
• Hazewinkel, Michiel, ed. (2001), "Kervaire invariant", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=k/k055350 
• Hazewinkel, Michiel, ed. (2001), "Dendritic manifold", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=d/d031010