Kervaire manifold

In mathematics, specifically in differential topology, a Kervaire manifold K⁴ⁿ⁺² is a piecewise-linear manifold of dimension 4n+2 constructed by Kervaire (1960) 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.