Computing cohomology groups that classify bundles of strongly self-absorbing $C^*$-algebras
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915713133838336 |
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| author | Dadarlat, Marius McClure, James E. Pennig, Ulrich |
| author_facet | Dadarlat, Marius McClure, James E. Pennig, Ulrich |
| contents | Locally trivial bundles of $C^*$-algebras with fibre $D \otimes \mathcal{K}$ for a strongly self-absorbing $C^*$-algebra $D$ over a finite CW-complex $X$ form a group $E^1_D(X)$ that is the first group of a cohomology theory $E^*_D(X)$. In this paper we compute these groups by expressing them in terms of ordinary cohomology and connective $K$-theory. To compare the $C^*$-algebraic version of $gl_1(KU)$ with its classical counterpart we also develop a uniqueness result for the unit spectrum of complex periodic topological $K$-theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08028 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Computing cohomology groups that classify bundles of strongly self-absorbing $C^*$-algebras Dadarlat, Marius McClure, James E. Pennig, Ulrich Operator Algebras Locally trivial bundles of $C^*$-algebras with fibre $D \otimes \mathcal{K}$ for a strongly self-absorbing $C^*$-algebra $D$ over a finite CW-complex $X$ form a group $E^1_D(X)$ that is the first group of a cohomology theory $E^*_D(X)$. In this paper we compute these groups by expressing them in terms of ordinary cohomology and connective $K$-theory. To compare the $C^*$-algebraic version of $gl_1(KU)$ with its classical counterpart we also develop a uniqueness result for the unit spectrum of complex periodic topological $K$-theory. |
| title | Computing cohomology groups that classify bundles of strongly self-absorbing $C^*$-algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2302.08028 |