The relative index in coarse index theory and submanifold obstructions to uniform positive scalar curvature

2025/06/17 by Alexander Engel, Engel, Alexander, Wulff, Christopher · 1 citation
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2506.14301

openalex publication_date 2025/06/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

We provide a coarse version of the relative index of Gromov and Lawson and thoroughly establish all of its basic properties. As an application, we discuss a general procedure to construct wrong way maps on the K-theory of the Roe algebra mapping the coarse index class of the Dirac operator of a manifold to the one of a suitably embedded submanifold of arbitrary codimension, thereby establishing an abstract machinery to find obstructions to uniform positive scalar curvature coming from these submanifolds.

Cited by

• Relative higher index theory on quotients of Roe algebras and positive scalar curvature at infinity

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