论文标题
定量K理论，正标曲率和带宽
Quantitative K-theory, positive scalar curvature, and band width
论文作者
论文摘要
我们在运算符$ k $的定量框架之间建立了两个连接 - 几何$ c^*$ - 代数和正标曲率问题。首先，我们引入了较高索引的定量概念，并使用它来使Rosenberg的众所周知的障碍物对封闭的旋转歧管上的正标曲率进行改进。我们表明，在具有统一正标曲率的多种流形上，狄拉克操作员索引消失的繁殖与曲率下限相关。其次，我们使用相关技术给格罗莫夫的带宽猜想提供了一种方法，这是Zeidler和Cecchini最近工作的主题。
We develop two connections between the quantitative framework of operator $K$-theory for geometric $C^*$-algebras and the problem of positive scalar curvature. First, we introduce a quantitative notion of higher index and use it to give a refinement of the well-known obstruction of Rosenberg to positive scalar curvature on closed spin manifolds coming from the higher index of the Dirac operator. We show that on a manifold with uniformly positive scalar curvature, the propagation at which the index of the Dirac operator vanishes is related inversely to the curvature lower bound. Second, we give an approach, using related techniques, to Gromov's band width conjecture, which has been the subject of recent work by Zeidler and Cecchini from a different point of view.
