剩余有限群盒空间的有界同构猜想

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Topology and Analysis Pub Date : 2021-03-31 DOI:10.1142/s1793525323500280

Markus Zeggel

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引用次数: 0

摘要

在本文中，我们研究了K理论法雷尔-琼斯猜想的一个粗糙版本，我们称之为粗糙或有界同构猜想。利用控制范畴理论，我们能够将渐近忠实覆盖的这个猜想转化为更熟悉的形式。这使得我们证明了具有系数的Farrell—Jones集合映射是同构的剩余有限群的盒空间的猜想。

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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The Bounded Isomorphism Conjecture for Box Spaces of Residually Finite Groups

In this article we study a coarse version of the $K$-theoretic Farrell--Jones conjecture we call coarse or bounded isomorphism conjecture. Using controlled category theory we are able to translate this conjecture for asymptotically faithful covers into a more familiar form. This allows us to prove the conjecture for box spaces of residually finite groups whose Farrell--Jones assembly map with coefficients is an isomorphism.

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来源期刊

Journal of Topology and Analysis MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.