Infinite connected sums, K-area and positive scalar curvature

2004/08/17 by Levi Lopes de Lima, de Lima, Levi Lopes
Mathematics · #53C21 #58J20 #58J32 #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0408228

openalex publication_date 2004/08/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02

Abstract

Whyte used the index theory of Dirac operators and Block-Weiberger uniformly finite homology to show that certain infinite connected sums do not carry a metric with nonnegative scalar curvature in their bounded geometry class. His proof uses a coarse version of the A-class to obstruct such metrics. In this note we prove a version of Whyte's result where a variant of the notion of infinite K-area, originally due to Gromov, is used to obstruct metrics with positive scalar curvature.

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