English

Fundamental groups of 3-dimensional small covers

Geometric Topology 2021-11-29 v1

Abstract

Small covers arising from 3-dimensional simple polytopes are an interesting class of 3-manifolds. The fundamental group is a rigid invariant for wide classes of 3-manifolds, particularly for orientable Haken manifolds, which include orientable small covers. By using Morse-theoretic approach we give a procedure to get an explicit, balanced presentation of the fundamental group of a closed, orientable 3-dimensional simple cover with minimal number of generators. Beside that the minimal Heegaard splitting is determined by this presentation.

Keywords

Cite

@article{arxiv.2111.13147,
  title  = {Fundamental groups of 3-dimensional small covers},
  author = {Vladimir Grujić},
  journal= {arXiv preprint arXiv:2111.13147},
  year   = {2021}
}
R2 v1 2026-06-24T07:52:15.121Z