On Self-mapping Degrees of $S^3$-geometry manifolds

TL;DR

This paper classifies all possible self-mapping degrees of 3-manifolds with $S^3$-geometry, contributing to the broader goal of understanding self-maps of all closed orientable 3-manifolds within Thurston's framework.

Contribution

It provides a complete determination of self-mapping degrees for $S^3$-geometry manifolds, expanding the understanding of self-maps in 3-manifold topology.

Findings

All self-mapping degrees of $S^3$-geometry manifolds are classified.

The results support the broader project of classifying self-maps of all closed orientable 3-manifolds.

The work advances understanding of the relationship between fundamental groups and self-mapping degrees.

Abstract

In this paper we determined all of the possible self mapping degrees of the manifolds with $S^3$-geometry, which are supposed to be all 3-manifolds with finite fundamental groups. This is a part of a project to determine all possible self mapping degrees of all closed orientable 3-manifold in Thurston's picture.