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Register a new userK-theory of Etesi C*-algebras
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Authors
Igor Nikolaev
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We study the $C^*$-algebra $mathbb{E}_{mathscr{M}}$ of a smooth 4-dimensional manifold $mathscr{M}$ introduced by Gabor 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 Gompfs 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 $mathbb{E}_{mathscr{M}}$.
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