The monoid of suspensions and loops modulo Bousfield equivalence

Volume 199 / 2008

Jeff Strom Fundamenta Mathematicae 199 (2008), 213-226 MSC: 55P60, 55P65, 55P99, 20M05. DOI: 10.4064/fm199-3-2


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.


  • Jeff StromDepartment of Mathematics
    Western Michigan University
    1903 W. Michigan Ave.
    Kalamazoo, MI 49008, U.S.A.

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