Kervaire manifold

In mathematics, specifically in differential topology, a Kervaire manifold ${\displaystyle K^{4n+2}}$ is a piecewise-linear manifold of dimension ${\displaystyle 4n+2}$ constructed by Michel Kervaire (1960) by plumbing together the tangent bundles of two ${\displaystyle (2n+1)}$-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, MR 0139172, S2CID 120977898
• Shtan'ko, M.A. (2001) [1994], "Kervaire invariant", Encyclopedia of Mathematics, EMS Press
• Shtan'ko, M.A. (2001) [1994], "Dendritic manifold", Encyclopedia of Mathematics, EMS Press