The Classification of Hyperelliptic Groups in Dimension 4

TL;DR

This paper provides a complete classification of hyperelliptic groups in four dimensions, expanding understanding of their structure using group and representation theory.

Contribution

It offers the first full classification of 4-dimensional hyperelliptic groups, a significant step in understanding hyperelliptic manifolds.

Findings

Complete list of hyperelliptic groups in dimension 4

Identification of group-theoretic properties of these groups

Application of representation theory to classify the groups

Abstract

Hyperelliptic manifolds are natural generalizations of hyperelliptic surfaces in dimensions. We provide a full classification of the groups, which arise as the holonomy group of a 4-dimensional hyperelliptic manifold. The classification is mostly based on group- and representation-theoretic methods.