Moduli spaces of flat Riemannian metrics on 4-dimensional closed manifolds

TL;DR

This paper characterizes the algebraic and topological structure of moduli spaces of flat Riemannian metrics on certain 4-dimensional closed flat manifolds with specific holonomy properties.

Contribution

It provides a detailed description of the moduli spaces for 4D flat manifolds with two or three generators in their holonomy, advancing understanding of their geometric classification.

Findings

Algebraic description of moduli spaces

Topological classification of moduli spaces

Explicit characterization for manifolds with specific holonomy generators

Abstract

We give the algebraic and topological description of the moduli spaces of flat metrics for the 4-dimensional closed flat manifolds with two or three generators in their holonomy.