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Realizing additive monoids as mapping degree sets

2026/07/30 by Cristina Costoya, Vicente Muñoz, Bruno Valverde-Morales +1
Mathematics · #math.AT #math.GT

paper · pdf

15 pages, no figures

arxiv created 2026/07/30 · arxiv updated 2026/07/31

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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