Manifolds with singularities accepting a metric, of positive scalar curvature

Abstract

We study the question of existence of a Riemannian metric of positive scalar curvature metric on manifolds with the Sullivan-Baas singularities. The manifolds we consider are Spin and simply connected. We prove an analogue of the Gromov-Lawson Conjecture for such manifolds in the case of particular type of singularities. We give an affirmative answer when such manifolds with singularities accept a metric of positive scalar curvature in terms of the index of the Dirac operator valued in the corresponding "K-theories with singularities". The key ideas are based on the construction due to Stolz, some stable homotopy theory, and the index theory for the Dirac operator applied to the manifolds with singularities. As a side-product we compute homotopy types of the corresponding classifying spectra.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper22.abs.html

References in corpus (2)

• A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture
• Groupoid C*-algebras and index theory on manifolds with singularities

Cited by in corpus (7)

• Groupoid C*-algebras and index theory on manifolds with singularities
• Positive scalar curvature on simply connected spin pseudomanifolds
• Positive scalar curvature on manifolds with fibered singularities
• Yamabe metrics on cylindrical manifolds
• Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants
• Positive scalar curvature on manifolds with odd order abelian fundamental groups
• Homotopy invariance of the space of metrics with positive scalar curvature on manifolds with singularities