Gorde:
| Egile Nagusiak: | , , |
|---|---|
| Formatua: | Preprint |
| Argitaratua: |
2023
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| Gaiak: | |
| Sarrera elektronikoa: | https://arxiv.org/abs/2302.08028 |
| Etiketak: |
Etiketa erantsi
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Aurkibidea:
- 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.