Universal Toda brackets of ring spectra

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dc.creatorSagave, Steffen
dc.date2006-11-27
dc.date2007-10-15
dc.date.accessioned2026-07-07T08:56:57Z
dc.date.available2026-07-07T08:56:57Z
dc.descriptionWe construct and examine the universal Toda bracket of a highly structured ring spectrum R. This invariant of R is a cohomology class in the Mac Lane cohomology of the graded ring of homotopy groups of R which carries information about R and the category of R-module spectra. It determines for example all triple Toda brackets of R and the first obstruction to realizing a module over the homotopy groups of R by an R-module spectrum. For periodic ring spectra, we study the corresponding theory of higher universal Toda brackets. The real and complex K-theory spectra serve as our main examples.
dc.description38 pages; a few typos corrected, to appear in Trans. Amer. Math. Soc
dc.identifierhttps://arxiv.org/abs/math/0611808
dc.identifierhttp://arxiv.org/abs/math/0611808
dc.identifierTrans. Amer. Math. Soc., 360(5):2767-2808, 2008.
dc.identifierdoi:10.1090/S0002-9947-07-04487-X
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146797
dc.subjectAlgebraic Topology
dc.subjectK-Theory and Homology
dc.subject55P43 (Primary); 19D55, 55S35, 55U35 (Secondary)
dc.titleUniversal Toda brackets of ring spectra
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