Differential Topology
Self-coincidence of mappings between spheres and the Strong Kervaire Invariant One Problem
Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 511-513.

Let f:S4n2S2n be a map between spheres of dimensions 4n2 and 2n with n>4. We show that the existence of such a map satisfying the property that the pair (f,f):S4n2S2n can be deformed to a coincidence free pair but cannot be deformed to coincidence free by small deformation is equivalent to the Strong Kervaire Invariant One Problem, i.e., the existence of an element of order 2 with Kervaire invariant one in the stable homotopy group π2n2s.

Soit f:S4n2S2n une application continue entre les sphères de dimensions respectives 4n2 et 2n pour n>4. Nous démontrons que, si la paire (f,f) est déformable en une paire libre de coïncidences, alors elle n'est pas déformable par petites déformations si et seulement si n=2j, j3, et l'invariant de Kervaire de la classe d'homotopie [f]π4n2(S2n) est 1. Cette dernière condition est équivalente à une forme forte du problème de Kervaire.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.01.016
Gonçalves, Daciberg 1; Randall, Duane 2

1 Departamento de Matemática, IME, USP, Caixa Postal 66.281, CEP, 05311-970, São Paulo, SP, Brazil
2 Department of Mathematics and Computer Science, Loyola University, 6363 St. Charles Avenue, New Orleans, LA 70118, USA
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Gonçalves, Daciberg; Randall, Duane. Self-coincidence of mappings between spheres and the Strong Kervaire Invariant One Problem. Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 511-513. doi : 10.1016/j.crma.2006.01.016. http://www.numdam.org/articles/10.1016/j.crma.2006.01.016/

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