TL;DR
This paper explores the connection between the vanishing of the A-hat genus and the geometric phenomenon of collapsing spin manifolds with bounded below curvature.
Contribution
It establishes new relationships linking topological invariants to geometric collapsing behavior in spin manifolds.
Findings
Vanishing of A-hat genus implies certain collapsing conditions.
Provides criteria for collapsing spin manifolds with curvature bounds.
Links topological invariants to geometric collapse scenarios.
Abstract
We give relationships between the vanishing of the A-hat genus and the possibility that a spin manifold can collapse with curvature bounded below.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology