Spines of 3-Manifolds as Polyhedra with Identified Faces

TL;DR

This paper explores the relationship between spines of 3-manifolds and polyhedra with identified faces, establishing a natural correspondence and equivalence with special spines.

Contribution

It demonstrates that spines of closed, orientable 3-manifolds can be represented by polyhedra with identified faces, and proves the equivalence with special spines.

Findings

Spines of 3-manifolds can be presented via polyhedra with identified faces.

Established the equivalence between special spines and certain polyhedra.

Provided new insights into the structure of 3-manifolds.

Abstract

In this article we establish the relation between the spines of 3-manifolds and the polyhedra with identified faces. We do this by showing that the spines of the closed, connected, orientable 3-manifolds can be presented through polyhedra with identified faces in a very natural way. We also prove the equivalence between the special spines and a certain type of polyhedra, and other related results.