Universal Toda brackets of ring spectra
Universal Toda brackets of ring spectra
Dokument öffnen (711.2KB)Art der Hochschulschrift
DissertationPrüfungsdatum
30.06.2006Datum der Veröffentlichung
2006Erstgutachter
Schwede, StefanZweitgutachter
Richter, BirgitMetadaten
Zur Langanzeige
Zitierbare Links 
Inhalt
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.
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.
Schlagwörter
stabile Homotopietheorie, Massey-Produkte, Modellkategorien, stable homotopy theory, Massey products, model categories
Klassifikation (DDC)
510 MathematikSagave, Steffen: Universal Toda brackets of ring spectra. - Bonn, 2006. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-08082
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-08082
@phdthesis{handle:20.500.11811/2639,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-08082,
author = {{Steffen Sagave}},
title = {Universal Toda brackets of ring spectra},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2006,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/2639}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-08082,
author = {{Steffen Sagave}},
title = {Universal Toda brackets of ring spectra},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2006,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/2639}
}
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