Invariance of Finiteness of K-area under Surgery

TL;DR

This paper investigates how the K-area invariant, which obstructs positive scalar curvature on Riemannian manifolds, behaves under surgical modifications of the manifold.

Contribution

It provides new insights into the invariance or variation of K-area when the manifold undergoes surgery, a fundamental geometric operation.

Findings

K-area's behavior under surgery is characterized.

Conditions under which K-area remains finite are identified.

Implications for scalar curvature obstructions are discussed.

Abstract

K-area is an invariant for Riemannian manifolds introduced by Gromov as an obstruction to the existence of positive scalar curvature. However in general it is difficult to determine whether K-area is finite or not. though the definition of K-area is quite natural. In this paper, we study how the invariant changes under surgery.