Fundamental groups of 3-dimensional small covers

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.