K-theory of Etesi C*-algebras
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866911389764812800 |
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| author | Nikolaev, Igor V. |
| author_facet | Nikolaev, Igor V. |
| contents | We study the $C^*$-algebra $\mathbb{E}_{\mathscr{M}}$ of a smooth 4-dimensional manifold $\mathscr{M}$ introduced by Gábor Etesi. It is proved that the $\mathbb{E}_{\mathscr{M}}$ is a stationary AF-algebra. We calculate the topological and smooth invariants of $\mathscr{M}$ in terms of the K-theory of the $C^*$-algebra $\mathbb{E}_{\mathscr{M}}$. Using Gompf's Stable Diffeomorphism Theorem, it is shown that all smoothings of $\mathscr{M}$ form a torsion abelian group. The latter is isomorphic to the Brauer group of a number field associated to the K-theory of $\mathbb{E}_{\mathscr{M}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_08237 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | K-theory of Etesi C*-algebras Nikolaev, Igor V. Geometric Topology Operator Algebras 46L85, 57K4 We study the $C^*$-algebra $\mathbb{E}_{\mathscr{M}}$ of a smooth 4-dimensional manifold $\mathscr{M}$ introduced by Gábor Etesi. It is proved that the $\mathbb{E}_{\mathscr{M}}$ is a stationary AF-algebra. We calculate the topological and smooth invariants of $\mathscr{M}$ in terms of the K-theory of the $C^*$-algebra $\mathbb{E}_{\mathscr{M}}$. Using Gompf's Stable Diffeomorphism Theorem, it is shown that all smoothings of $\mathscr{M}$ form a torsion abelian group. The latter is isomorphic to the Brauer group of a number field associated to the K-theory of $\mathbb{E}_{\mathscr{M}}$. |
| title | K-theory of Etesi C*-algebras |
| topic | Geometric Topology Operator Algebras 46L85, 57K4 |
| url | https://arxiv.org/abs/2012.08237 |