KK- and E-theory via homotopy theory
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910471006715904 |
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| author | Bunke, Ulrich |
| author_facet | Bunke, Ulrich |
| contents | We provide a homotopy theorist's point of view on $KK$- and $E$-theory for $C^{*}$-algebras. We construct stable $\infty$-categories representing these theories through a sequence of Dwyer-Kan localizations of the category of $C^{*}$-algebras. Thereby we will reveal the homotopic theoretic meaning of various classical construction from $C^{*}$-algebra theory, in particular of Cuntz' $q$-construction. We will also discuss operator algebra $K$-theory in this framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_12607 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | KK- and E-theory via homotopy theory Bunke, Ulrich K-Theory and Homology Algebraic Topology Operator Algebras We provide a homotopy theorist's point of view on $KK$- and $E$-theory for $C^{*}$-algebras. We construct stable $\infty$-categories representing these theories through a sequence of Dwyer-Kan localizations of the category of $C^{*}$-algebras. Thereby we will reveal the homotopic theoretic meaning of various classical construction from $C^{*}$-algebra theory, in particular of Cuntz' $q$-construction. We will also discuss operator algebra $K$-theory in this framework. |
| title | KK- and E-theory via homotopy theory |
| topic | K-Theory and Homology Algebraic Topology Operator Algebras |
| url | https://arxiv.org/abs/2304.12607 |