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.

See also

• Exotic sphere

References

• Kervaire, M. (1960), "A manifold which does not admit any differentiable structure", Comm. Math. Helv., 34: 257–270, doi:10.1007/BF02565940, MR 0139172 
• Shtan'ko, M.A. (2001), "Kervaire invariant", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4 
• Shtan'ko, M.A. (2001), "Dendritic manifold", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4