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Universal Toda brackets of ring spectra

Steffen Sagave
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Abstract

We 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.

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Steffen Sagave. 2007-10-15. Universal Toda brackets of ring spectra. https://doi.org/10.1090/s0002-9947-07-04487-x

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