A variant of Roe algebras for spaces with cylindrical ends with applications in relative higher index theory

Journal of noncommutative geometry

article

Mehran Seyedhosseini¹ 

[1] Universität Potsdam

关键词: Positive scalar curvature;    higher index theory;    rho-invariants;    Roe algebras;    manifolds with cylindrical ends;    manifolds with boundary;   

DOI  :  10.4171/jncg/457

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

In this paper, we define a variant of Roe algebras for spaces with cylindrical ends and use this to study questions regarding existence and classification of metrics of positive scalar curvature on such manifolds which are collared on the cylindrical end. We discuss how our constructions are related to relative higher index theory as developed by Chang, Weinberger, and Yu and use this relationship to define higher rho-invariants for positive scalar curvature metrics on manifolds with boundary. This paves the way for the classification of these metrics. Finally, we use the machinery developed here to give a concise proof of a result of Schick and the author, which relates the relative higher index with indices defined in the presence of positive scalar curvature on the boundary.

【 授权许可】

CC BY