Self-mapping degrees of torus bundles and torus semi-bundles

TL;DR

This paper determines the set of degrees of all self-maps for torus bundles and semi-bundles, advancing the classification of self-mapping degrees in 3-manifold topology.

Contribution

It explicitly computes the self-mapping degree sets for torus bundles and semi-bundles, enriching the understanding of their self-maps within Thurston's framework.

Findings

Determined D(M) for all torus bundles.

Determined D(M) for all torus semi-bundles.

Detailed analysis of semi-bundle structures.

Abstract

Each closed oriented 3-manifold $M$ is naturally associated with a set of integers $D(M)$, the degrees of all self-maps on $M$. $D(M)$ is determined for each torus bundle and torus semi-bundle $M$. The structure of torus semi-bundle is studied in detail. The paper is a part of a project to determine $D(M)$ for all 3-manifolds in Thurston's picture.