Index theory with bounded geometry, the uniformly finite A-hat class, and infinite connected sums

2004/05/14 by Kevin Whyte
Mathematics · #math.DG

paper · pdf

published as JDG 59, 2001

arxiv created 2004/05/14 · arxiv updated 2009/12/01

Abstract

We analyze the obstruction to metrics of positive scalar curvature within a given bounded distortion class of metrics. This obstruction lives in a non-Hausdorff cohomology group Poincare dual to the uniformly finite homology studied by Block and Weinberger. One of the applications is a converse to their theorem on infinite connected sums, giving a complete picture of when such manifolds have metrics of positive scalar curvature.

Related

• Infinite connected sums, K-area and positive scalar curvature
• A relative higher index theorem, diffeomorphisms and positive scalar curvature
• Index theory and deformations of open nonnegatively curved manifolds
• Relative higher index theory on quotients of Roe algebras and positive scalar curvature at infinity
• Positive scalar curvature, K-area and essentialness