度量空间自由积的粗糙几何

IF 0.9 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2025-09-03 DOI:10.1016/j.bulsci.2025.103721

Qin Wang, Jvbin Yao

{"title":"度量空间自由积的粗糙几何","authors":"Qin Wang, Jvbin Yao","doi":"10.1016/j.bulsci.2025.103721","DOIUrl":null,"url":null,"abstract":"<div><div>Recently, a notion of the free product <span><math><mi>X</mi><mo>⁎</mo><mi>Y</mi></math></span> of two metric spaces <em>X</em> and <em>Y</em> has been introduced by T. Fukaya and T. Matsuka in their study of the coarse Baum-Connes conjecture. In this paper, we study coarse geometric permanence properties of the free product <span><math><mi>X</mi><mo>⁎</mo><mi>Y</mi></math></span>. We show that if <em>X</em> and <em>Y</em> satisfy any of the following conditions, then <span><math><mi>X</mi><mo>⁎</mo><mi>Y</mi></math></span> also satisfies that condition: (1) they are coarsely embeddable into a Hilbert space or a uniformly convex Banach space; (2) they have Yu's Property A; (3) they are hyperbolic spaces. These generalize the corresponding results for discrete groups to the case of metric spaces.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103721"},"PeriodicalIF":0.9000,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Coarse geometry of free products of metric spaces\",\"authors\":\"Qin Wang, Jvbin Yao\",\"doi\":\"10.1016/j.bulsci.2025.103721\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Recently, a notion of the free product <span><math><mi>X</mi><mo>⁎</mo><mi>Y</mi></math></span> of two metric spaces <em>X</em> and <em>Y</em> has been introduced by T. Fukaya and T. Matsuka in their study of the coarse Baum-Connes conjecture. In this paper, we study coarse geometric permanence properties of the free product <span><math><mi>X</mi><mo>⁎</mo><mi>Y</mi></math></span>. We show that if <em>X</em> and <em>Y</em> satisfy any of the following conditions, then <span><math><mi>X</mi><mo>⁎</mo><mi>Y</mi></math></span> also satisfies that condition: (1) they are coarsely embeddable into a Hilbert space or a uniformly convex Banach space; (2) they have Yu's Property A; (3) they are hyperbolic spaces. These generalize the corresponding results for discrete groups to the case of metric spaces.</div></div>\",\"PeriodicalId\":55313,\"journal\":{\"name\":\"Bulletin des Sciences Mathematiques\",\"volume\":\"206 \",\"pages\":\"Article 103721\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin des Sciences Mathematiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0007449725001472\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin des Sciences Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0007449725001472","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

最近，T. Fukaya和T. Matsuka在他们对粗糙Baum-Connes猜想的研究中引入了两个度量空间X和Y的自由积X Y的概念。本文研究了自由积X * Y的粗几何持久性。我们证明了如果X和Y满足下列任何条件，则X Y也满足该条件：(1)它们可以粗嵌入到Hilbert空间或一致凸Banach空间中；（二）拥有于某财产A的；(3)它们是双曲空间。这些结果将离散群的相应结果推广到度量空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Coarse geometry of free products of metric spaces

Recently, a notion of the free product

X ⁎ Y

of two metric spaces X and Y has been introduced by T. Fukaya and T. Matsuka in their study of the coarse Baum-Connes conjecture. In this paper, we study coarse geometric permanence properties of the free product

X ⁎ Y

. We show that if X and Y satisfy any of the following conditions, then

X ⁎ Y

also satisfies that condition: (1) they are coarsely embeddable into a Hilbert space or a uniformly convex Banach space; (2) they have Yu's Property A; (3) they are hyperbolic spaces. These generalize the corresponding results for discrete groups to the case of metric spaces.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊