# Positive scalar curvature on foliations: the enlargeability

## TL;DR

This paper extends Gromov and Lawson's nonexistence result for positive scalar curvature from enlargeable manifolds to foliations, avoiding index theorems on noncompact manifolds.

## Contribution

It generalizes the positive scalar curvature obstruction to foliations, broadening the scope beyond manifolds without relying on index theory.

## Key findings

- Positive scalar curvature cannot exist on enlargeable foliations.
- The method avoids using index theorems on noncompact manifolds.
- Extends classical results to a broader geometric context.

## Abstract

We generalize the famous result of Gromov and Lawson on the nonexistence of metric of positive scalar curvature on enlargeable manifolds to the case of foliations, without using index theorems on noncompact manifolds.