arXiv subjects

Bartira Maués

Publications and source records attributed to Bartira Maués.

2 recordsLinked to original sources

arXiv2026

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

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.

math.AT↗

arXiv2025

Computation of the Nielsen fixed point number for 2-valued non-split maps on the Klein bottle

In this paper we study 2-valued non-split maps, focusing on the Klein bottle. We establish a connection between a 2-valued non-split map $ϕ:X\multimap Y$ and a pair of classes of maps $([f],[f\circ δ])\in [\tilde X,Y]\times[\tilde X, Y]$, where $δ$ is a free involution on $\tilde X$, $X=\tilde X/δ$ and the class of the lift factor $[f]$ does not satisfy the Borsuk-Ulam Property in respect to $δ$. We also exhibit a method to compute the Nielsen fixed point number of a 2-valued non-split map on a closed connected manifold in terms of the Nielsen coincidence number between a lift factor and a covering space map, generalizing the formula from only orientable manifolds to also non-orientable manifolds. Finally we display a formula for the Nielsen fixed point number of 2-valued non-split maps on the Klein bottle in terms of two braids of the Klein bottle.

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