An equivariant Poincaré duality for proper cocompact actions by matrix groups

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Noncommutative Geometry Pub Date : 2020-09-29 DOI:10.4171/jncg/468

Haoyang Guo, V. Mathai

引用次数: 1

Abstract

Let $G$ be a linear Lie group acting properly and isometrically on a $G$-spin$^c$ manifold $M$ with compact quotient. We show that Poincare duality holds between $G$-equivariant $K$-theory of $M$, defined using finite-dimensional $G$-vector bundles, and $G$-equivariant $K$-homology of $M$, defined through the geometric model of Baum and Douglas.

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矩阵群适当共紧作用的等变Poincaré对偶

设$G$是一个线性李群，它在具有紧致商的$G$-自旋$^c$流形$M$上正等距作用。我们证明了Poincare对偶在$G$的$G$-等变$K$-理论和$M$的$G-等变$K$-同调之间成立，这两个理论是用有限维$G$向量丛定义的，这两种理论是用Baum和Douglas的几何模型定义的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.