Geodesic
Topological Localization, Category and Cocategory
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 319-322

Voir la notice de l'article provenant de la source Cambridge University Press

It is easy to see that a localization (in the sense of [9]) of a simply connected co H-space (equivalently a simply connected space of Liusternik-Schnirelman category one) is again a co H-space. (All spaces in this paper will be pointed and have the based homotopy type of a connected CW complex; and all maps will preserve base-points.) We show that the category of a simply connected space does not increase on localizing. We give an example to show that the hypothesis simple-connectivity is crucial. In strong contrast, the dual result only requires connectivity. 
Toomer, Graham Hilton. Topological Localization, Category and Cocategory. Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 319-322. doi: 10.4153/CJM-1975-038-4
@article{10_4153_CJM_1975_038_4,
     author = {Toomer, Graham Hilton},
     title = {Topological {Localization,} {Category} and {Cocategory}},
     journal = {Canadian journal of mathematics},
     pages = {319--322},
     year = {1975},
     volume = {27},
     number = {2},
     doi = {10.4153/CJM-1975-038-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-038-4/}
}
TY  - JOUR
AU  - Toomer, Graham Hilton
TI  - Topological Localization, Category and Cocategory
JO  - Canadian journal of mathematics
PY  - 1975
SP  - 319
EP  - 322
VL  - 27
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-038-4/
DO  - 10.4153/CJM-1975-038-4
ID  - 10_4153_CJM_1975_038_4
ER  - 
%0 Journal Article
%A Toomer, Graham Hilton
%T Topological Localization, Category and Cocategory
%J Canadian journal of mathematics
%D 1975
%P 319-322
%V 27
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-038-4/
%R 10.4153/CJM-1975-038-4
%F 10_4153_CJM_1975_038_4

[1] 1. Berstein, I. and Hilton, P. J., Category and generalized Hopf invariants, Illinois J. Math. 4 (1960), 437–451. Google Scholar

[2] 2. Bousfield, A. K. and Kan, D. M., Homotopy limits, completions and localizations, Springer Lectures Notes No. 304. Google Scholar

[3] 3. Ganea, T., Liusternik-Schnirelmann category and strong category, Illinois J. Math. 11 (1967), 417–427. Google Scholar

[4] 4. Ganea, T., A generalization of the homology and homotopy suspension, Comment. Math. Helv. 89 (1967), 295–322. Google Scholar

[5] 5. Ganea, T., Sur quelques invariants numériques du type d'homotopie, Thèse, Faculté des Sciences de Paris, Mai, 1962. Google Scholar

[6] 6. Ganea, T., Some problems on numerical homotopy invariants, Springer Lecture Notes No. 249. Google Scholar

[7] 7. James, I. M., Reduced product spaces, Ann. of Math. 62 (1955), 170–197. Google Scholar

[8] 8. Serre, J.-P., Homologie singulière des espaces fibres, Applications, Ann. of Math. S4- (1951), 425–505. Google Scholar

[9] 9. Sullivan, D., Geometric topology, Part I, M.I.T., mimeographed notes, June, 1970. Google Scholar

[10] 10. Svarc, A. S., The genus of a fibre space, Amer. Math. Soc. Transi. 55 (1966), 49–140. Google Scholar

Cité par Sources :