论文标题
$ C^*$ - 代数的L理论
L-theory of $C^*$-algebras
论文作者
论文摘要
我们为实际$ c^*$ - 代数的L理论频谱建立了一个公式，从中，我们根据拓扑K组来从中推断出L组的介绍，从而扩展了所有以前已知的此类结果。一路上，我们将整体比较映射$τ\ colon \ mathrm {k} \延长到\ Mathrm {l} $在前两位作者在先前工作中获得的\ Mathrm {l} $，以实现真实的$ C^*$ - 代数 - 并使用拓扑grothendieck-witt理论来解释它。最后，我们利用结果对Baum-Connes的猜想和L Wheoretic Farrell-Jones的猜想进行了整体比较，并就方向的歧管上的签名运算符讨论了我们的比较映射$τ$。
We establish a formula for the L-theory spectrum of real $C^*$-algebras from which we deduce a presentation of the L-groups in terms of the topological K-groups, extending all previously known results of this kind. Along the way, we extend the integral comparison map $τ\colon \mathrm{k} \to \mathrm{L}$ obtained in previous work by the first two authors to real $C^*$-algebras and interpret it using topological Grothendieck-Witt theory. Finally, we use our results to give an integral comparison between the Baum-Connes conjecture and the L-theoretic Farrell-Jones conjecture, and discuss our comparison map $τ$ in terms of the signature operator on oriented manifolds.
