Leafwise positive scalar curvature and the Rosenberg index

TL;DR

This paper proves that for a closed spin manifold with a foliation and a leafwise positive scalar curvature metric, the Rosenberg index must be zero, linking geometric curvature conditions to topological invariants.

Contribution

It establishes a new connection between leafwise positive scalar curvature and the vanishing of the Rosenberg index on spin manifolds.

Findings

Rosenberg index is zero under leafwise positive scalar curvature

Foliation structure influences topological invariants

Links geometry with topological index theory

Abstract

Let $M$ be a closed spin manifold, in this paper, we show that if there is a foliation $(M,F)$ and a Riemannian metric on $M$ that has leafwise positive scalar curvature then the Rosenberg index of $M$ is zero.