{"title":"黎曼曲面和直角阿廷群的深度","authors":"Yves Félix, Steve Halperin","doi":"10.1007/s40062-019-00250-3","DOIUrl":null,"url":null,"abstract":"<p>We consider two families of spaces, <i>X</i>: the closed orientable Riemann surfaces of genus <span>\\(g>0\\)</span> and the classifying spaces of right-angled Artin groups. In both cases we compare the depth of the fundamental group with the depth of an associated Lie algebra, <i>L</i>, that can be determined by the minimal Sullivan algebra. For these spaces we prove that </p><p>and give precise formulas for the depth.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 1","pages":"223 - 248"},"PeriodicalIF":0.5000,"publicationDate":"2019-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00250-3","citationCount":"2","resultStr":"{\"title\":\"The depth of a Riemann surface and of a right-angled Artin group\",\"authors\":\"Yves Félix, Steve Halperin\",\"doi\":\"10.1007/s40062-019-00250-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We consider two families of spaces, <i>X</i>: the closed orientable Riemann surfaces of genus <span>\\\\(g>0\\\\)</span> and the classifying spaces of right-angled Artin groups. In both cases we compare the depth of the fundamental group with the depth of an associated Lie algebra, <i>L</i>, that can be determined by the minimal Sullivan algebra. For these spaces we prove that </p><p>and give precise formulas for the depth.</p>\",\"PeriodicalId\":636,\"journal\":{\"name\":\"Journal of Homotopy and Related Structures\",\"volume\":\"15 1\",\"pages\":\"223 - 248\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2019-11-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s40062-019-00250-3\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Homotopy and Related Structures\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-019-00250-3\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Homotopy and Related Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-019-00250-3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The depth of a Riemann surface and of a right-angled Artin group
We consider two families of spaces, X: the closed orientable Riemann surfaces of genus \(g>0\) and the classifying spaces of right-angled Artin groups. In both cases we compare the depth of the fundamental group with the depth of an associated Lie algebra, L, that can be determined by the minimal Sullivan algebra. For these spaces we prove that
期刊介绍：
Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences.
Journal of Homotopy and Related Structures is intended to publish papers on
Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.
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