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.