Zusammenfassung
Continuing our project on noncommutative (stable) homotopywe construct symmetric monoidal infinity-categorical models for separable C*-algebras SC infinity* and noncommutative spectra NSp using the framework of Higher Algebra due to Lurie. We study smashing (co) localizations of SC infinity* and NSp with respect to strongly self-absorbing C*-algebras. We analyse the homotopy categories of the ...
Zusammenfassung
Continuing our project on noncommutative (stable) homotopywe construct symmetric monoidal infinity-categorical models for separable C*-algebras SC infinity* and noncommutative spectra NSp using the framework of Higher Algebra due to Lurie. We study smashing (co) localizations of SC infinity* and NSp with respect to strongly self-absorbing C*-algebras. We analyse the homotopy categories of the localizations of SC infinity* and give universal characterizations thereof. We construct a stable infinity-categorical model for bivariant connective E-theory and compute the connective E-theory groups of 0(infinity)-stable C*-algebras. We also introduce and study the nonconnective version of Quillen's nonunital K'-theory in the framework of stable infinity-categories. This is done in order to promote our earlier result relating topological T-duality to noncommutative motives to the infinity-categorical setup. Finally, we carry out some computations in the case of stable and 0(infinity)-stable C*-algebras.
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