Comptes Rendus
no. 10
Differential geometry
On the rank of a product of manifolds
[Sur le rang d'un produit de variétés]

Présenté par : Étienne Ghys

Francisco-Javier Turiel1 ; Arthur G. Wasserman2
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, Volume 354 (2016) no. 10, pp. 1023-1025.

Cette note donne un exemple de deux variétés compactes M et N pour lesquelles le rang de M×N est strictement plus grand que rangM+rangN.

This note gives an example of closed smooth manifolds M and N for which the rank of M×N is strictly greater than rankM+rankN.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.08.004

Francisco-Javier Turiel 1 ; Arthur G. Wasserman 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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Francisco-Javier Turiel; Arthur G. Wasserman. On the rank of a product of manifolds. Comptes Rendus. Mathématique, Volume 354 (2016) no. 10, pp. 1023-1025. doi : 10.1016/j.crma.2016.08.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.08.004/

[1] G. Chatelet; H. Rosenberg Manifolds which admit Rn actions, Publ. Math. Inst. Hautes Études Sci., Volume 43 (1974), pp. 245-260

[2] S.P. Novikov 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] H. Rosenberg Singularities of R2 actions, Topology, Volume 7 (1968), pp. 143-145

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

[5] D. Tischler Manifolds Mn of rank n−1, Proc. Amer. Math. Soc., Volume 94 (1985), pp. 158-160

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