Kervaire manifold

In mathematics, specifically in differential topology, a Kervaire manifold K 4 n + 2 {\displaystyle K^{4n+2}} is a piecewise-linear manifold of dimension 4 n + 2 {\displaystyle 4n+2} constructed by Michel Kervaire (1960) by plumbing together the tangent bundles of two ( 2 n + 1 ) {\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
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