Comptes Rendus
no. 10
Differential geometry
On the rank of a product of manifolds
Presented by: Étienne Ghys
Francisco-Javier Turiel1; Arthur G. Wasserman2
1Geometría y Topología, Facultad de Ciencias, Campus de Teatinos, s/n, 29071, Málaga, Spain
2University of Michigan, Ann Arbor, MI 48109-1003, USA
Comptes Rendus. Mathématique, Volume 354 (2016) no. 10, pp. 1023-1025

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.

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.

Received:
Accepted:
Published online:
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 
@article{CRMATH_2016__354_10_1023_0,
     author = {Francisco-Javier Turiel and Arthur G. Wasserman},
     title = {On the rank of a product of manifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1023--1025},
     year = {2016},
     publisher = {Elsevier},
     volume = {354},
     number = {10},
     doi = {10.1016/j.crma.2016.08.004},
     language = {en},
}
TY  - JOUR
AU  - Francisco-Javier Turiel
AU  - Arthur G. Wasserman
TI  - On the rank of a product of manifolds
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 1023
EP  - 1025
VL  - 354
IS  - 10
PB  - Elsevier
DO  - 10.1016/j.crma.2016.08.004
LA  - en
ID  - CRMATH_2016__354_10_1023_0
ER  - 
%0 Journal Article
%A Francisco-Javier Turiel
%A Arthur G. Wasserman
%T On the rank of a product of manifolds
%J Comptes Rendus. Mathématique
%D 2016
%P 1023-1025
%V 354
%N 10
%I Elsevier
%R 10.1016/j.crma.2016.08.004
%G en
%F CRMATH_2016__354_10_1023_0
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

[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

Cited by Sources:

Comments - Policy