Geodesic
Spaces with complexity one
Homology, homotopy, and applications, Tome 21 (2019) no. 2, pp. 23-26.

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

An $A$-cellular space is a space built from a space A and its suspensions, analogous to the way that $CW$-complexes are built from $S^0$ and its suspensions. The $A$-cellular approximation of a space $X$ is an $A$-cellular space $C W_A X$, which is closest to $X$ among all $A$-cellular spaces. The $A$-complexity of a space $X$ is an ordinal number that quantifies how difficult it is to build an $A$-cellular approximation of $X$. In this paper, we study spaces with low complexity. In particular, we show that if $A$ is a sphere localized at a set of primes then the $A$-complexity of each space $X$ is at most $1$.
DOI : 10.4310/HHA.2019.v21.n2.a2
Classification : 18C10, 55P60
Keywords: cellular space, complexity, mapping space 
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Alyson Bittner. Spaces with complexity one. Homology, homotopy, and applications, Tome 21 (2019) no. 2, pp. 23-26. doi : 10.4310/HHA.2019.v21.n2.a2. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n2.a2/

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