Geodesic
(Co)homology self-closeness numbers of simply-connected spaces
Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 1-16.

Voir la notice de l'article provenant de la source International Press of Boston

The (co)homology self-closeness number of a simply-connected based CW-complex $X$ is the minimal number $k$ such that any self-map $f$ of $X$ inducing an automorphism of the (co)homology groups for dimensions $\leqslant k$ is a self-homotopy equivalence. These two numbers are homotopy invariants and have a close relation with the group of self-homotopy equivalences. In this paper, we compare the (co)homology self-closeness numbers of spaces in certain cofibrations, define the $\operatorname{mod} p$ (co)homology self-closeness number of simply-connected $p$-local spaces with finitely generated homologies and study some properties of the $(\operatorname{mod} p)$ (co)homology self-closeness numbers.
DOI : 10.4310/HHA.2021.v23.n1.a1
Classification : 55P05, 55P10
Keywords: self-homotopy equivalence, self-closeness number, cofibration 
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     author = {Pengcheng Li},
     title = {(Co)homology self-closeness numbers of simply-connected spaces},
     journal = {Homology, homotopy, and applications},
     pages = {1--16},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2021},
     doi = {10.4310/HHA.2021.v23.n1.a1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n1.a1/}
}
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Pengcheng Li. (Co)homology self-closeness numbers of simply-connected spaces. Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 1-16. doi : 10.4310/HHA.2021.v23.n1.a1. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n1.a1/

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