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Comptes Rendus Mathématique
Volume 352, n° 3
pages 251-254 (mars 2014)
Doi : 10.1016/j.crma.2014.01.013
Received : 15 October 2013 ;  accepted : 17 January 2014
On the vanishing of the Lannes–Zarati homomorphism
Sur l'annulation de l'homomorphisme de Lannes–Zarati
 

Nguyễn H.V. Hưng , Võ T.N. Quỳnh , Ngô A. Tuấn
 Department of Mathematics, Vietnam National University, Hanoi, 334 Nguyễn Trãi Street, Hanoi, Viet Nam 

Abstract

The conjecture on spherical classes states that the Hopf invariant one and the Kervaire invariant one classes are the only elements in   belonging to the image of the Hurewicz homomorphism. The Lannes–Zarati homomorphism is a map that corresponds to an associated graded (with a certain filtration) of the Hurewicz map. The algebraic version of the conjecture predicts that the s -th Lannes–Zarati homomorphism vanishes in any positive stems for  . In the article, we prove the conjecture for the fifth Lannes–Zarati homomorphism.

The full text of this article is available in PDF format.
Résumé

La conjecture sur les classes sphériques affirme que les classes détectées par l'invariant de Hopf et l'invariant de Kervaire sont les seules dans   dans l'image de l'homomorphisme de Hurewicz. L'homomorphisme de Lannes–Zarati est l'application correspondant au gradué (pour une certaine filtration) de l'homomorphisme de Hurewicz. La version algébrique de la conjecture prédit que le s -ième homomorphisme de Lannes–Zarati s'annule en tout degré positif pour  . Dans cette note, nous démontrons la conjecture pour le cinquième homomorphisme de Lannes–Zarati.

The full text of this article is available in PDF format.

 The work was supported in part by a Grant of the NAFOSTED.



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