Gromov-Lawson余维2对正标量曲率的阻碍与C *指数

Yosuke Kubota, Thomas Schick Riken, Japan., Mathematisches Institut, Universitat Gottingen
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引用次数: 5

摘要

Gromov和Lawson为闭合自旋流形M开发了一种协维2指数阻碍正标量曲率的方法,后来由Hanke、Pape和Schick改进。Kubota也证明了这种阻碍也可以从M的基本群的极大C*-代数的k理论中取值的周围流形M的Rosenberg指数中得到,使用相对指数结构。在这篇笔记中,我们稍微简化了Kubota的工作,并指出它也适用于签名算子,从而恢复了Higson, Schick, Xie的余维2子流形的高签名的同伦不变性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Gromov–Lawson codimension 2 obstruction to positive scalar curvature and the C∗–index
Gromov and Lawson developed a codimension 2 index obstruction to positive scalar curvature for a closed spin manifold M, later refined by Hanke, Pape and Schick. Kubota has shown that also this obstruction can be obtained from the Rosenberg index of the ambient manifold M which takes values in the K-theory of the maximal C*-algebra of the fundamental group of M, using relative index constructions. In this note, we give a slightly simplified account of Kubota's work and remark that it also applies to the signature operator, thus recovering the homotopy invariance of higher signatures of codimension 2 submanifolds of Higson, Schick, Xie.
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