从微分的角度研究拓扑结构群的高不变量的可加性

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Noncommutative Geometry Pub Date : 2020-05-28 DOI:10.4171/jncg/369

Baojie Jiang, Hongzhi Liu

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引用次数: 1

摘要

在[14]中，Weinberger, Xie和Yu用分段线性方法证明了与同伦等价相关的高不变量定义了从拓扑结构群到解析结构群的群同态，即若干几何C * -代数的k理论。本文利用Weinberger、Xie和Yu的部分成果，从微分几何的角度证明了拓扑结构群上与同伦等价相关的高不变量映射的可加性。数学学科分类(2010)。58 j22。

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Additivity of higher rho invariant for the topological structure group from a differential point of view

In [14], Weinberger, Xie and Yu proved that higher rho invariant associated to homotopy equivalence defines a group homomorphism from the topological structure group to analytic structure group, K-theory of certain geometric C∗-algebras, by piecewise-linear approach. In this paper, we adapt part of Weinberger, Xie and Yu’s work, to give a differential geometry theoretic proof of the additivity of the map induced by higher rho invariant associated to homotopy equivalence on topological structure group. Mathematics Subject Classification (2010). 58J22.

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来源期刊

Journal of Noncommutative Geometry 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative geometry and its applications to other fields of mathematics and theoretical physics. Topics covered include in particular: Hochschild and cyclic cohomology K-theory and index theory Measure theory and topology of noncommutative spaces, operator algebras Spectral geometry of noncommutative spaces Noncommutative algebraic geometry Hopf algebras and quantum groups Foliations, groupoids, stacks, gerbes Deformations and quantization Noncommutative spaces in number theory and arithmetic geometry Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory, gravity, mirror symmetry, solid state physics, statistical mechanics.