A Note on the Category of the Telescope
Canadian mathematical bulletin, Tome 20 (1977) no. 1, p. 107
Voir la notice de l'article provenant de la source Cambridge University Press
Let X be an infinite connected CW-complex which is the union of an increasing sequence of subcomplexes Xr . Let cat X denote the Lusternik-Schnirelmann category of X, normalized to take the value 0 on contractible spaces. Suppose that cat Xr ≤ K (r ≥ 1). In his problem list [1], T. Ganea proved that cat Xr ≤ 2k +1 and asked (Problem 5) whether this is the best possible upper bound. The purpose of this note is to prove that cat X ≤ 2k.
Hardie, K. A. A Note on the Category of the Telescope. Canadian mathematical bulletin, Tome 20 (1977) no. 1, p. 107. doi: 10.4153/CMB-1977-018-4
@article{10_4153_CMB_1977_018_4,
author = {Hardie, K. A.},
title = {A {Note} on the {Category} of the {Telescope}},
journal = {Canadian mathematical bulletin},
pages = {107--107},
year = {1977},
volume = {20},
number = {1},
doi = {10.4153/CMB-1977-018-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-018-4/}
}
[1] 1. Ganea, T., Some problems on numerical homotopy invariants. Symposium on Algebraic Topology, Battelle Seattle Research Centre 1971, Lecture Notes in Mathematics 249, Springer-Verlag, Berlin, 1971. Google Scholar
[2] 2. Hardie, K. A., On the category of the double mapping cylinder, Töhoku Mathematical Journal, 25 (1973), 355-358. Google Scholar
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