The suspension and loop space functors, Σ and Ω, operate on the lattice of Bousfield classes of (sufficiently highly connected) topological spaces, and therefore generate a submonoid ℒ of the complete set of operations on the Bousfield lattice. We determine the structure of ℒ in terms of a single parameter of homotopy theory which is closely tied to the problem of desuspending weak cellular inequalities.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm199-3-2,
author = {Jeff Strom},
title = {The monoid of suspensions and loops modulo Bousfield equivalence},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {213-226},
zbl = {1145.55010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm199-3-2}
}
Jeff Strom. The monoid of suspensions and loops modulo Bousfield equivalence. Fundamenta Mathematicae, Tome 201 (2008) pp. 213-226. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm199-3-2/