# Positive scalar curvature on manifolds with odd order abelian fundamental groups

## TL;DR

This paper develops a theory for positive scalar curvature metrics on manifolds with certain singularities and applies it to construct such metrics on specific nonspin, atoral manifolds with odd order abelian fundamental groups, solving a longstanding conjecture.

## Contribution

It introduces a new homology invariance principle for positive scalar curvature on singular manifolds and constructs metrics on a new class of nonspin, atoral manifolds with finite fundamental groups.

## Key findings

- Constructed positive scalar curvature metrics on nonspin, atoral manifolds with odd order abelian fundamental groups
- Proved the Gromov-Lawson-Rosenberg conjecture for this class of manifolds
- Developed a homology invariance principle for manifolds with Baas-Sullivan singularities

## Abstract

We introduce Riemannian metrics of positive scalar curvature on manifolds with Baas-Sullivan singularities, prove a corresponding homology invariance principle and discuss admissible products. Using this theory we construct positive scalar curvature metrics on closed smooth manifolds of dimension at least five which have odd order abelian fundamental groups, are nonspin and atoral. This solves the Gromov-Lawson-Rosenberg conjecture for a new class of manifolds with finite fundamental groups.