Monopole Bundles over Fuzzy Complex Projective Spaces

TL;DR

This paper constructs monopole bundles over fuzzy complex projective spaces using projective modules, calculates their Chern classes, and shows they converge to classical monopole charges as the representation size increases.

Contribution

It introduces a novel construction of monopole bundles on fuzzy spaces and computes their topological invariants, bridging noncommutative and classical geometry.

Findings

Chern classes match classical monopole charges in the large N limit

Monopole bundles are realized as projective modules over fuzzy spaces

Provides explicit calculations connecting noncommutative and classical topological invariants

Abstract

We give a construction of the monopole bundles over fuzzy complex projective spaces as projective modules. The corresponding Chern classes are calculated. They reduce to the monopole charges in the N -> infinity limit, where N labels the representation of the fuzzy algebra.