Kervaire manifold

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