Finite sets containing zero are mapping degree sets

TL;DR

This paper proves that any finite set of integers containing zero can be realized as the set of mapping degrees between two oriented closed connected manifolds, extending the result to rational numbers.

Contribution

It provides a positive solution to the problem of realizing finite sets containing zero as mapping degree sets, including in the rational case.

Findings

Any finite integer set containing zero is a mapping degree set.

The result extends to rational numbers.

The paper confirms the existence of manifolds with prescribed degree sets.

Abstract

In this paper we solve in the positive the question of whether any finite set of integers, containing the zero, is the mapping degree set between two oriented closed connected manifolds of the same dimension. We extend this question to the rational setting, where an affirmative answer is also given.