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arXiv · 2609.34013

A study of $n$-valued non-split maps and applications

Daciberg Lima Gonçalves·Bartira Maués·Daniel Vendrúscolo
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Abstract

For a given $n$-valued map, there exists a suitable minimal covering of the domain such that the composition of this covering with the map yields a split map, composed of $n$ single-valued maps, called the lift factors. Using the group action of the deck-transformation group we construct intermediate covering spaces as well as intermediate configuration spaces, allowing the original map to lift to these spaces, building a tower to illustrate at which level the lift factors split off. We then display two applications of these new tools. The first is to derive results concerning the Borsuk-Ulam property for certain coverings of the tower. The second is to obtain a sharp formula for the Nielsen number of an $n$-valued non-split map, using the coincidence number of specific single-valued maps that arise in the lifts of the tower.

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Daciberg Lima Gonçalves, Bartira Maués, Daniel Vendrúscolo. 2026-09-27. A study of $n$-valued non-split maps and applications. https://arxiv.org/abs/2609.34013

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