论文标题
Etesi c*-ergebras的K理论
K-theory of Etesi C*-algebras
论文作者
论文摘要
我们研究$ c^*$ - 代数$ \ Mathbb {e} _ {\ Mathscr {m}} $的平滑4维歧管$ \ Mathscr {M Mathscr {m} $由GáborEtesi引入。事实证明，$ \ mathbb {e} _ {\ mathscr {m}} $是固定的af-algebra。我们根据$ c^*$ - algebra $ \ mathbb {e} _ {\ mathscr {m}} $的k理论计算$ \ mathscr {m} $的拓扑和平滑不变性。使用GOMPF的稳定差异定理，显示出$ \ mathscr {m} $的所有平滑符构成一个扭转的Abelian组。后者是与$ \ mathbb {e} _ {\ Mathscr {m}} $相关的数字字段的Brauer组的同构。
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 $\mathbb{E}_{\mathscr{M}}$.
