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Relations amongst Toda brackets and the Kervaire invariant in dimension 62. (English) Zbl 0606.55010
In this paper we use relations amongst Toda brackets and a lot of detailed information about the homotopy groups of spheres to show that there exists a 62-dimensional framed manifold with Kervaire invariant one. This paper, together with others [Contemp. Math. 19, 9-22 (1983; Zbl 0528.55010); ”The Kervaire invariant and the Hopf invariant”, preprint, Warwick Univ. (1982)] represents an effort to supply full details for a number of the results announced by the third author [Algebraic Topology, Proc. Symp. Pure Math. 22, 165-169 (1971; Zbl 0241.55018)], and to explore further some of the ideas behind that paper.

55Q40 Homotopy groups of spheres
55Q35 Operations in homotopy groups
57R60 Homotopy spheres, Poincaré conjecture
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