Classification of generalized Seifert fiber spaces
Geometric Topology
2026-04-13 v2 Differential Geometry
Metric 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 -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.
Keywords
Cite
@article{arxiv.2409.02216,
title = {Classification of generalized Seifert fiber spaces},
author = {Fernando Galaz-Garcia and Jesús Núñez-Zimbrón},
journal= {arXiv preprint arXiv:2409.02216},
year = {2026}
}
Comments
We have corrected the statement and proof of Theorem B. The previous version had an incorrect value for the Euler number of the Seifert manifold appearing as double branched cover of a generalized Seifert manifold. To illustrate the main changes we have added several examples in this direction. 9 pages. To appear at the Canadian Mathematical Bulletin