Universal Toda brackets of ring spectra
Algebraic Topology
2008-01-29 v3 K-Theory and Homology
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.
Cite
@article{arxiv.math/0611808,
title = {Universal Toda brackets of ring spectra},
author = {Steffen Sagave},
journal= {arXiv preprint arXiv:math/0611808},
year = {2008}
}
Comments
38 pages; a few typos corrected, to appear in Trans. Amer. Math. Soc