On Some Aspects of Linear Connections in Noncommutative Geometry

TL;DR

This paper explores metric and linear connections within noncommutative geometry, specifically applying these concepts to a hybrid space combining continuous and discrete elements, advancing understanding of geometric structures in noncommutative settings.

Contribution

It introduces and compares two approaches to metric and linear connections in noncommutative geometry, with applications to mixed continuous-discrete spaces.

Findings

Comparison of two connection concepts in noncommutative geometry

Application to product spaces of continuous and discrete geometries

Insights into geometric structures in noncommutative settings

Abstract

We discuss two concepts of metric and linear connections in noncommutative geometry, applying them to the case of the product of continuous and discrete (two-point) geometry.