Spaces with complexity one

DOI10.4310/HHA.2019.V21.N2.A2zbMATH Open1433.55006arXiv1712.04009MaRDI QIDQ2326298

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Publication date: 7 October 2019

Published in: (Search for Journal in Brave)

Abstract: An $A$-cellular space is a space built from $A$ and its suspensions, analogously 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.

Full work available at URL: https://arxiv.org/abs/1712.04009

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