The topology of the Eisenstein-Picard modular surface

TL;DR

This paper determines the global topological structure of the Eisenstein-Picard modular surface, a complex hyperbolic space quotient, as a 4-orbifold, providing insights into its geometric and topological properties.

Contribution

It explicitly describes the global topology of the Eisenstein-Picard modular surface as a 4-orbifold, a novel result in the study of complex hyperbolic quotients.

Findings

The surface is a 4-orbifold with explicitly characterized topology.

The quotient space is identified as the Eisenstein-Picard modular surface.

The topological structure is fully determined and described.

Abstract

The Eisenstein-Picard modular surface $M$ is the quotient space of the complex hyperbolic plane by the modular group $\rm PU(2,1; \mathbb{Z}[\omega])$. We determine the global topology of $M$ as a 4-orbifold.