Classification of generalized Seifert fiber spaces

TL;DR

This paper offers a symbolic classification of generalized Seifert fiber spaces and analyzes their double branched covers, contributing to the understanding of collapsing Alexandrov 3-spaces.

Contribution

It introduces a symbolic classification framework for generalized Seifert fiber spaces and characterizes their double branched covers as Seifert manifolds.

Findings

Double branched cover of a non-manifold generalized Seifert fiber space is a Seifert manifold

Provides symbolic invariants in terms of original space's invariants

Classifies generalized Seifert fiber spaces in the context of Alexandrov geometry

Abstract

We provide a symbolic classification of generalized Seifert fiber spaces, which were introduced by Mitsuishi and Yamaguchi in the classification of collapsing Alexandrov $3$-spaces. Additionally, we show that the canonical double branched cover of a non-manifold generalized Seifert fiber space is a Seifert manifold and compute its symbolic invariants in terms of those of the original space.