The image of Singer's fourth transfer

Hu'ng, Nguyễn H.V.; Quy`nh, Võ T.N.

doi:10.1016/j.crma.2009.10.018

Topology

The image of Singer's fourth transfer
[L'image du quatrième transfert de Singer]

Présenté par : Christophe Soulé

Hu'ng, Nguyễn H.V.¹ ; Quy`nh, Võ T.N.¹

¹ Department of Mathematics, Vietnam National University, Hanoi, 334 Nguyễn Trãi Street, Hanoi, Vietnam

Comptes Rendus. Mathématique, Tome 347 (2009) no. 23-24, pp. 1415-1418.

Résumé
Abstract

Dans cette Note on achève la description du quatriéme transfert de Singer, complétant ainsi le travail de nombreux auteurs. Plus précisement on montre que chaque élément de la famille ${p_{i} | i ⩾ 0}$ appartient à l'image du quatriéme transfert. Combinant cela avec des résultats antérieurs de R. Bruner, L.M. Hà, T.N. Nam, et du premier auteur, on en déduit que l'image du transfert algébrique contient chaque élément des quatre familles ${d_{i} | i ⩾ 0}$ , ${e_{i} | i ⩾ 0}$ , ${f_{i} | i ⩾ 0}$ , et ${p_{i} | i ⩾ 0}$ , et ne contient aucun élément des trois familles ${g_{i} | i ⩾ 1}$ , ${D_{3} (i) | i ⩾ 0}$ , and ${p_{i}^{'} | i ⩾ 0}$ .

La méthode utilisée pour montrer que des éléments sont dans l'image du transfert peut être appliquée non seulement à la famille $p_{i}$ mais aussi aux familles $d_{i}$ , $e_{i}$ , and $f_{i}$ .

We complete in this Note the description of Singer's fourth transfer, already studied by many authors. More precisely, we show that each element of the family ${p_{i} | i ⩾ 0}$ belongs to the image of this fourth transfer. Combining this with previous results by R. Bruner, L.M. Hà, T.N. Nam and the first author, we deduce that the image of the algebraic transfer contains all the elements of the families ${d_{i} | i ⩾ 0}$ , ${e_{i} | i ⩾ 0}$ , ${f_{i} | i ⩾ 0}$ and ${p_{i} | i ⩾ 0}$ , but none from the families ${g_{i} | i ⩾ 1}$ , ${D_{3} (i) | i ⩾ 0}$ and ${p_{i}^{'} | i ⩾ 0}$ .

The method used to prove that elements are in the transfer's image can be applied not only to the family of $p_{i}$ 's but to the families of $d_{i}$ 's, $e_{i}$ 's and $f_{i}$ 's as well.

Reçu le : 2009-04-13
Accepté le : 2009-10-14
Publié le : 2009-11-12

DOI : 10.1016/j.crma.2009.10.018

Affiliations des auteurs :

Hu'ng, Nguyễn H.V. ¹ ; Quy`nh, Võ T.N. ¹

¹ Department of Mathematics, Vietnam National University, Hanoi, 334 Nguyễn Trãi Street, Hanoi, Vietnam

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Hu'ng, Nguyễn H.V.; Quy`nh, Võ T.N. The image of Singer's fourth transfer. Comptes Rendus. Mathématique, Tome 347 (2009) no. 23-24, pp. 1415-1418. doi : 10.1016/j.crma.2009.10.018. http://www.numdam.org/articles/10.1016/j.crma.2009.10.018/

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Cité par Sources :

^☆ The work was supported in part by a grant of the NAFOSTED.