Positive curvature, partial vanishing theorems, and coarse indices

2012/10/23 by John Roe, Roe, John · 2 citations
Mathematics · #19K56 (Primary) 46L80 #58J22 (Secondary) #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #K-Theory and Homology (math.KT) #Metric Geometry (math.MG) #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1210.6100

openalex publication_date 2012/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a complete Riemannian manifold, D a Dirac-type operator on M whose Weitzenbock curvature is uniformly positive on the complement of a subset Z of M. We show that the coarse index of D is localized to the K-theory of the coarse C*-algebra of Z. Applications are discussed, including a coarse form of the relative index theorem.

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• Relative higher index theory on quotients of Roe algebras and positive scalar curvature at infinity
• Equivariant Localization of K-homological Euler Class for almost connected Lie Groups

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