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Two conjectures on spherical classes and on the squaring operation.

Le : 20/10/2014 14h00
Par : Nguyễn H. V. Hưng (VNU, Hanoi et LAREMA)
Lieu : I 103
Lien web :
Résumé : The conjecture on spherical classes states that the Hopf invariant one and the Kervaire invariant one classes are the only elements which are detected by the Hurewicz homomorphism. The Lannes-Zarati homomorphism is a map that corresponds to an associated graded (with a certain filtration) of the Hurewicz map. We discuss our algebraic version of the conjecture predicting that the Lannes-Zarati homomorphism of s indeterminates vanishes in any positive degrees for s>2. Several particular cases of the conjecture have been proved. We also discuss our second conjecture predicting that the length of any finite $Sq0$-family in the cohomology of the Steenrod algebra is equally bounded by a rather small number that only depends on the homological degree or the family. The conjecture is closely related to Singer’s conjecture stating that the algebraic transfer is a monomorphism.