Isospectral Deformations of Eguchi-Hanson Spaces as Nonunital Spectral Triples

TL;DR

This paper investigates how Eguchi-Hanson spaces can be deformed into noncommutative geometries via spectral triples, focusing on their geometric and analytic properties in a noncompact setting.

Contribution

It introduces a framework for isospectral deformations of Eguchi-Hanson spaces as nonunital spectral triples, linking geometric conditions to noncommutative spin manifolds.

Findings

Established conditions for locality, smoothness, and summability of the spectral triples.

Connected geometric properties of Eguchi-Hanson spaces to noncommutative spin geometry.

Provided insights into noncompact noncommutative geometric structures.

Abstract

We study the isospectral deformations of the Eguchi-Hanson spaces along a torus isometric action in the noncompact noncommutative geometry. We concentrate on locality, smoothness and summability conditions of the nonunital spectral triples, and relate them to the geometric conditions to be noncommutative spin manifolds.