On Stable Diffeomorphism of Exotic Spheres in the Metastable Range

Antonelli, P. L.

Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 579-587

Résumé

Let ⊖n p+ 1 denote the subgroup of the Kervaire-Milnor group θn consisting of those n-spheres which imbed with trivial normal bundle in Euclidean (n + p + 1)-space, n < 2p. It is known that such imbeddings always exist [6], and that the normal bundle is independent of the imbedding [10]. Following [2], we write Ωn,p for the quotient θ n /⊖n p+ 1.The order of Ωn,p after identifying each element with its inverse, is equal to the number of diffeomorphically distinct (orientation preserved) Σn × Sp [2; 5]. Indeed, Ωn,p is closely linked to the problem of determining the number of smooth structures α(n, p) on Sn × Sp. For instance, if Ωn,p = 0 then α(n, p) equals the order of θn+p [5]. Specific results are easily read off Table I and Theorem 2.1.

Détail

DOI : 10.4153/CJM-1971-065-x

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