The monoid of suspensions and loops modulo Bousfield equivalence
Volume 199 / 2008
Fundamenta Mathematicae 199 (2008), 213-226
MSC: 55P60, 55P65, 55P99, 20M05.
DOI: 10.4064/fm199-3-2
Abstract
The suspension and loop space functors, $\mit\Sigma$ and $\mit\Omega$, operate on the lattice of Bousfield classes of (sufficiently highly connected) topological spaces, and therefore generate a submonoid ${\mathcal L}$ of the complete set of operations on the Bousfield lattice. We determine the structure of ${\mathcal L}$ in terms of a single parameter of homotopy theory which is closely tied to the problem of desuspending weak cellular inequalities.
