Enlargeability, foliations, and positive scalar curvature

• 成果类型: Article
• 署名作者: Benameur, Moulay-Tahar; Heitsch, James L.
• 署名单位: Universite de Montpellier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0829-6
• 发表日期: 2019
• 页码: 367-382
• 关键词: Manifolds

摘要

We extend the deep and important results of Lichnerowicz, Connes, and Gromov-Lawson which relate geometry and characteristic numbers to the existence and non-existence of metrics of positive scalar curvature (PSC). In particular, we show: that a spin foliation with Hausdorff homotopy groupoid of an enlargeable manifold admits no PSC metric; that any metric of PSC on such a foliation is bounded by a multiple of the reciprocal of the foliation K-area of the ambient manifold; and that Connes' vanishing theorem for characteristic numbers of PSC foliations extends to a vanishing theorem for Haefliger cohomology classes.