A manifold which does not admit any differentiable structure

@article{Kervaire1960AMW,
  title={A manifold which does not admit any differentiable structure},
  author={M. Kervaire},
  journal={Commentarii Mathematici Helvetici},
  year={1960},
  volume={34},
  pages={257-270}
}
  • M. Kervaire
  • Published 1960
  • Mathematics
  • Commentarii Mathematici Helvetici
The Kervaire invariant in homotopy theory
In this note we discuss how the first author came upon the Kervaire invariant question while analyzing the image of the J-homomorphism in the EHP sequence. One of the central projects of algebraicExpand
Michel Kervaire work on knots in higher dimensions
The aim of this paper is to present Michel Kervaire’s work on differential knots in higher dimensions in codimension q = 2. In order to appreciate the importance of Kervaire’s contribution, weExpand
The Arf-Kervaire Invariant of framed manifolds
This work surveys classical and recent advances around the existence of exotic differentiable structures on spheres and its connection to stable homotopy theory.
HOMOTOPICALLY EQUIVALENT SMOOTH MANIFOLDS. I
In this paper we introduce a method for the investigation of smooth simply connected manifolds of dimension n ≥ 5 that permits a classification of them with exactness up to orientation-preservingExpand
The Kervaire invariant and surgery theory
We give an expository account of the development of the Kervaire invariant and its generalizations with emphasis on its applications to surgery and, in particular, to the existence of stablyExpand
Mod Two Homology and Cohomology
Introduction.- Simplicial (co)homology.- Singular and cellular (co)homologies.- Products.- Poincar'e Duality.- Projective spaces.- Equivariant cohomology.- Steenrod squares.- Stiefel-WhitneyExpand
The Arf-Kervaire invariant of framed manifolds as an obstruction to embeddability
We define a quadratic form which gives an obstruction to embedding N 4k+2 � R 6k+4 of a smooth highly connected manifold into Euclidean space, with sufficiently many nondegenerate sections of theExpand
...
1
2
3
4
5
...

References

SHOWING 1-9 OF 9 REFERENCES
DIFFERENTIABLE STRUCTURES ON SPHERES.
According to [5] the sphere S7 can be given several differentiable structures which are essentially distinct. A corresponding result for the 15-sphere has been proved by Shimada [10] and Tamura [12].Expand
RELATIVE CHARACTERISTIC CLASSES.
In the proof, we shall make use of a not quite classical form of Whitney duality, involving Stiefel-Whitney characteristic classes which have to be considered as relative cohomology classes. SinceExpand
Quelques propriétés globales des variétés différentiables
Le présent article donne la démonstration des résultats que j'ai annoncés dans quatre Notes aux Comptes-Rendus [28]1). Il est divisé en quatre chapitres. Le premier chapitre élabore une techniqueExpand
Cohomologie modulo 2 des complexes d’Eilenberg-MacLane
On sait que les complexes K (/7, q) introduits par Eilenberg-MacLane dans [4] jouent un r61e essentiel dans un grand nombre de questions de topologie alg6brique. Le pr6sent article est uneExpand
NOTE ON SUSPENSION