Finiteness of mapping degree sets for 3-manifolds

TL;DR

This paper investigates conditions under which the set of mapping degrees between closed orientable 3-manifolds is finite, providing a complete answer to a specific question in 3-manifold topology.

Contribution

It completes the classification of 3-manifold pairs for which the degree set is finite, using constructed maps to resolve an open question.

Findings

Identifies all pairs of 3-manifolds with finite degree sets

Constructs specific maps to demonstrate finiteness or infiniteness

Provides a comprehensive answer to the finiteness question in 3-manifold mappings

Abstract

By constructing certain maps, this note completes the answer of the Question: For which closed orientable 3-manifold $N$, the set of mapping degrees $\c{D}(M,N)$ is finite for any closed orientable 3-manifold $M$?