Realizing additive monoids as mapping degree sets

Cristina Costoya; Vicente Muñoz; Bruno Valverde-Morales; Antonio Viruel

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arXiv · 2607.27993

Realizing additive monoids as mapping degree sets

Cristina Costoya·Vicente Muñoz·Bruno Valverde-Morales·Antonio Viruel

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Abstract

We prove that mapping degree sets are stable under multiplication by finite subsets of $\mathbb Z$ containing $0$ and by sets obtained from additive submonoids of $\mathbb Z$ through finitely many sums and products. In particular, every set of the latter type occurs as a mapping degree set. As a consequence, we obtain a broad family of infinite mapping degree sets, including finite unions of arithmetic progressions starting at $0$. These results extend previous work on the realization problem and are related to a question posed by Neofytidis, Wang, and Wang.

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BibTeX RIS

Cristina Costoya, Vicente Muñoz, Bruno Valverde-Morales, Antonio Viruel. 2026-07-30. Realizing additive monoids as mapping degree sets. https://arxiv.org/abs/2607.27993

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