Nondurable K-theory equivalence and Bousfield localization

Lisa Langsetmo, Don Stanley

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5 Scopus citations

Abstract

In this paper we consider what happens when Adams self maps are modified by adding certain unstable maps. The unstable maps which are added are trivial after a single suspension. We can choose the modification so that the maps are still K-theory equivalences but the loops on the map are no longer K-theory equivalences. As a corollary we note that the maps are K-theory equivalences but not v1-periodic equivalences. Another consequence is the behavior of the cobar spectral sequences for generalized homology theories. Tamaki shows that in certain cases a cobar-type spectral sequence for generalized homology theories is well behaved. The maps we construct give an example where despite the connectivity of the spaces the cobar spectral sequence is still poorly behaved. Finally we use our maps to construct spaces whose Bousfield class is distinct from the cofiber of the Adams map but which becomes the same after one suspension.

Original languageEnglish (US)
Pages (from-to)397-410
Number of pages14
JournalK-Theory
Volume24
Issue number4
DOIs
StatePublished - Dec 2001

Keywords

  • Bousfield class
  • Inert set
  • K-theory

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