统一罗伊代数在n上的酉群的同伦类型

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Topology and Analysis Pub Date : 2021-04-07 DOI:10.1142/S1793525321500357

Tsuyoshi Kato, D. Kishimoto, Mitsunobu Tsutaya

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引用次数: 3

摘要

研究了[公式:见文]的一致Roe代数[公式:见文]的酉群空间[同伦型]。我们证明了稳定映射[公式:见正文]是一个同伦等价。此外，当[公式:见文]时，我们确定了[公式:见文]的同伦类型，它是Roe代数[公式:见文]的酉群[公式:见文](根据[公式:见文]的奇偶性，具有[公式:见文]或[公式:见文]的同伦类型)与有理性Eilenberg-MacLane空间的乘积。

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Homotopy type of the unitary group of the uniform Roe algebra on ℤn

We study the homotopy type of the space of the unitary group [Formula: see text] of the uniform Roe algebra [Formula: see text] of [Formula: see text]. We show that the stabilizing map [Formula: see text] is a homotopy equivalence. Moreover, when [Formula: see text], we determine the homotopy type of [Formula: see text], which is the product of the unitary group [Formula: see text] (having the homotopy type of [Formula: see text] or [Formula: see text] depending on the parity of [Formula: see text]) of the Roe algebra [Formula: see text] and rational Eilenberg–MacLane spaces.

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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.