Barnea, Ilan and Joachim, Michael and Mahanta, Snigdhayan (2017) Model structure on projective systems of C*-algebras and bivariant homology theories. NEW YORK JOURNAL OF MATHEMATICS, 23. pp. 383-439. ISSN 1076-9803,
Full text not available from this repository. (Request a copy)Abstract
Using the machinery of weak fibration categories due to Schlank and the first author, we construct a convenient model structure on the pro-category of separable C*-algebras Pro(SC*). The opposite of this model category models the infinity-category of pointed noncommutative spaces NS* defined by the third author. Our model structure on Pro(SC*) extends the well-known category of fibrant objects structure on SC*. We show that the pro-category Pro(SC*) also contains, as a full coreflective subcategory, the category of pro-C*-algebras that are cofiltered limits of separable C*-algebras. By stabilizing our model category we produce a general model categorical formalism for triangulated and bivariant homology theories of C*-algebras (or, more generally, that of pointed noncommutative spaces), whose stable infinity-categorical counterparts were constructed earlier by the third author. Finally, we use our model structure to develop a bivariant K-theory for all projective systems of separable C*-algebras generalizing the construction of Bonkat and show that our theory naturally agrees with that of Bonkat under some reasonable assumptions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | KK-THEORY; HOMOTOPY-THEORY; NONCOMMUTATIVE SPECTRA; ACCESSIBILITY RANK; WEAK EQUIVALENCES; PRO-CATEGORIES; COMPLEXES; SPACES; IDEAL; Pro-category; model category; infinity-category; triangulated category; bivariant homology; KK-theory; C*-algebra |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 12:57 |
| Last Modified: | 27 Feb 2019 14:34 |
| URI: | https://pred.uni-regensburg.de/id/eprint/77 |
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