Parametrized Morse Theory and Positive Scalar Curvature

TL;DR

This paper employs parametrized Morse theory and cobordism categories to analyze the homotopy type of positive scalar curvature metrics on high-dimensional spin manifolds, providing new proofs and extensions of recent results.

Contribution

It introduces a novel approach using cobordism categories and parametrized Morse theory to study positive scalar curvature metrics, extending previous theorems.

Findings

Alternative proof of Botvinnik, Ebert, and Randal-Williams' theorem

Extension of the homotopy type analysis to higher dimensions

New methods for understanding scalar curvature metrics

Abstract

We use the cobordism category constructed in arXiv:1703.01047 to the study the homotopy type of the space of positive scalar curvature metrics on a spin manifold of dimension > 4. Our methods give an alternative proof and extension of a recent theorem of Botvinnik, Ebert, and Randal-Williams from arXiv:1411.7408.