Geodesic
Homotopy self-equivalences of highly connected manifolds
Sbornik. Mathematics, Tome 41 (1982) no. 4, pp. 481-494 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper the sequence of Kahn is proved to decompose by almost diffeomorphisms, if the dimension of the manifold is not divisible by 8. The structure of the group of homotopy self-equivalences of $S^n\times S^n$ is calculated. Application of the bijection of Sullivan yields additional information. Bibliography: 13 titles. 
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     author = {V. E. Kolosov},
     title = {Homotopy self-equivalences of highly connected manifolds},
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V. E. Kolosov. Homotopy self-equivalences of highly connected manifolds. Sbornik. Mathematics, Tome 41 (1982) no. 4, pp. 481-494. http://geodesic.mathdoc.fr/item/SM_1982_41_4_a3/

[1] S. Smale, “On the structure of manifolds”, Amer. J. Math., 84 (1962), 387–399 | DOI | MR | Zbl

[2] J. Milnor, “A procedure for killing the homotopy groups of manifolds”, Simposia in Pure Math., 3, Amer. Math. Soc., 1961, 39–55 | MR

[3] C. T. C. Wall, “Classification of ($n-1$)-connected $2n$-manifolds”, Ann. Math., 75 (1962), 163–189 | DOI | MR | Zbl

[4] M. Kervaire, J. Milnor, “Groups of homotopy spheres”, Ann. Math., 77 (1963), 504–537 | DOI | MR | Zbl

[5] W. Browder, Surgery on the simply connected manifolds, Springer-Verlag, 1972 | MR

[6] P. Mosher, M. Tangora, Kogomologicheskie operatsii i ikh prilozheniya v teorii gomotopii, izd-vo “Mir”, Moskva, 1970 | MR

[7] P. J. Kahn, “Self-equivalences of ($n-1$)-connected $2n$-manifolds”, Math. Ann., 180 (1969), 26–47 | DOI | MR | Zbl

[8] S. Smale, “On the structure of $5$-manifolds”, Ann. Math., 75 (1962), 38–46 | DOI | MR | Zbl

[9] R. S. Palais, “Local triviality of the restriction map for embeddings”, Comm. Math. Helv., 34 (1960), 305–312 | DOI | MR | Zbl

[10] A. Haefliger, “Differentiable embeddings of $S^n$ in $S^{n+q}$ for $q>2$”, Ann. Math., 83 (1966), 402–436 | DOI | MR | Zbl

[11] Rurk, Sanderson, Vvedenie v kusochno lineinuyu topologiyu, izd-vo “Mir”, Moskva

[12] R. Penrous, J. Whitehead, E. Zeeman, “Imbeddings of manifolds”, Ann. Math., 73 (1961), 613–623 | DOI | MR

[13] P. J. Hilton, “On the homotopy groups of the union of spheres”, J. London Math. Soc., 30 (1955), 154–172 | DOI | MR | Zbl