On the rank of a product of manifolds

Turiel, Francisco-Javier; Wasserman, Arthur G.

doi:10.1016/j.crma.2016.08.004

Differential geometry

On the rank of a product of manifolds
[Sur le rang d'un produit de variétés]

Présenté par : Étienne Ghys

Turiel, Francisco-Javier ¹ ; Wasserman, Arthur G.²

¹ Geometría y Topología, Facultad de Ciencias, Campus de Teatinos, s/n, 29071, Málaga, Spain
² University of Michigan, Ann Arbor, MI 48109-1003, USA

Comptes Rendus. Mathématique, Tome 354 (2016) no. 10, pp. 1023-1025.

Résumé
Abstract

Cette note donne un exemple de deux variétés compactes M et N pour lesquelles le rang de $M \times N$ est strictement plus grand que $rang M + rang N$ .

This note gives an example of closed smooth manifolds M and N for which the rank of $M \times N$ is strictly greater than $rank M + rank N$ .

Reçu le : 2016-06-16
Accepté le : 2016-08-30
Publié le : 2016-09-06

DOI : 10.1016/j.crma.2016.08.004

Affiliations des auteurs :

Turiel, Francisco-Javier ¹ ; Wasserman, Arthur G. ²

¹ Geometría y Topología, Facultad de Ciencias, Campus de Teatinos, s/n, 29071, Málaga, Spain
² University of Michigan, Ann Arbor, MI 48109-1003, USA

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     title = {On the rank of a product of manifolds},
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     pages = {1023--1025},
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Turiel, Francisco-Javier; Wasserman, Arthur G. On the rank of a product of manifolds. Comptes Rendus. Mathématique, Tome 354 (2016) no. 10, pp. 1023-1025. doi : 10.1016/j.crma.2016.08.004. http://www.numdam.org/articles/10.1016/j.crma.2016.08.004/

Bibliographie
Cité par

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[2] Novikov, S.P. The topology summer institute, Seattle, USA, 1963 (Russ. Math. Surv.), Volume 20 (1965), pp. 145-167 http://www.mi.ras.ru/~snovikov/16.pdf

[3] Rosenberg, H. Singularities of $R^{2}$ actions, Topology, Volume 7 (1968), pp. 143-145

[4] Rosenberg, H.; Roussarie, R.; Weil, D. A classification of closed oriented 3-manifold of rank two, Ann. of Math. (2), Volume 91 (1970), pp. 449-464

[5] Tischler, D. Manifolds $M^{n}$ of rank $n - 1$ , Proc. Amer. Math. Soc., Volume 94 (1985), pp. 158-160

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