Universal Toda brackets of ring spectra
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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.References
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Additional Information
- Steffen Sagave
- Affiliation: Department of Mathematics, University of Oslo, Box 1053, N-0316 Oslo, Norway
- Email: sagave@math.uio.no
- Received by editor(s): December 5, 2006
- Published electronically: December 11, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 2767-2808
- MSC (2000): Primary 55P43; Secondary 19D55, 55S35, 55U35
- DOI: https://doi.org/10.1090/S0002-9947-07-04487-X
- MathSciNet review: 2373333