2020/12/15 by Igor Nikolaev, Nikolaev, Igor V.
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2012.08237
We study the C^*-algebra 𝔼_\mathscrM of a smooth 4-dimensional manifold \mathscrM introduced by Gábor Etesi. It is proved that the 𝔼_\mathscrM is a stationary AF-algebra. We calculate the topological and smooth invariants of \mathscrM in terms of the K-theory of the C^*-algebra 𝔼_\mathscrM. Using Gompf's Stable Diffeomorphism Theorem, it is shown that all smoothings of \mathscrM form a torsion abelian group. The latter is isomorphic to the Brauer group of a number field associated to the K-theory of 𝔼_\mathscrM.