Homology of finite K-area

TL;DR

This paper introduces a new homology theory based on Gromov's K-area that captures obstructions to enlargeability and relates to positive scalar curvature results on manifolds.

Contribution

It defines a generalized homology theory using K-area, providing a new perspective on obstructions to enlargeability and scalar curvature.

Findings

K-area homology encodes obstructions to enlargeability.

Rephrases classical results on positive scalar curvature.

Provides a new tool for geometric topology and scalar curvature studies.

Abstract

We use Gromov's K--area to define a generalized homology theory on compact smooth manifolds. In fact, this theory collects obstructions to the enlargeability of the manifold and its nontrivial submanifolds. Moreover, using the K--area homology we can rephrase some classic results about positive scalar curvature.