A study of n-valued non-split maps and applications
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.
Related
- Topological point singularities of manifold-valued maps and approximability by smooth maps
- Half-delocalization for semiclassical measures of split higher-dimensional quantum cat maps
- Semilinear Neumann boundary value problems for measure-valued maps
- A relaxation to the post-composition approach to metric-valued Sobolev maps
- Nielsen coincidence theory of (n,m)-valued pairs of maps
BibTeX
@misc{goncalves2026study,
title = {{A study of $n$-valued non-split maps and applications}},
author = {Daciberg Lima Gonçalves and Bartira Maués and Daniel Vendrúscolo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34013},
eprint = {2609.34013},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34013},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A study of n-valued non-split maps and applications
AU - Daciberg Lima Gonçalves
AU - Bartira Maués
AU - Daniel Vendrúscolo
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.34013
UR - https://arxiv.org/abs/2609.34013
AB - 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.
ER -