Homology, Homotopy and Applications
Volume 21 (2019)
Spaces with complexity one
Pages: 23 – 26
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 $1$.
cellular space, complexity, mapping space
2010 Mathematics Subject Classification
Copyright © 2018, Alyson Bittner. Permission to copy for private use granted.
Received 5 February 2018
Received revised 6 September 2018
Published 19 December 2018