arXiv subjects

Lore De Weerdt

Publications and source records attributed to Lore De Weerdt.

5 recordsLinked to original sources

arXiv2026

Nielsen coincidence theory for $(n,1)$-valued pairs

We generalise Nielsen theory to coincidences of pairs $(f,g)$ where $f:X\multimap Y$ is $n$-valued multimap and $g:X\to Y$ is a single-valued map, for $X$ and $Y$ closed oriented triangulable manifolds of equal dimension. We prove a Wecken theorem in this setting, and formulas for the Nielsen, Lefschetz and Reidemeister numbers in terms of the analogous invariants for single-valued maps. If $X$ and $Y$ are orientable infra-nilmanifolds, we derive explicit formulas in terms of the fundamental group morphisms of $f$ and $g$.

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arXiv2026

Nielsen numbers of $n$-valued maps on infra-solvmanifolds

We derive a formula for the Nielsen number $N(f)$ for every $n$-valued self-map $f$ of an infra-solvmanifold. To do this, we express $N(f)$ in terms of Nielsen coincidence numbers of single-valued maps on solvmanifolds, and derive a formula for Nielsen coincidence numbers in that setting.

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arXiv2026

An averaging formula for Nielsen numbers of affine n-valued maps on infra-nilmanifolds

In [8,9], the authors developed a nice formula to compute the Nielsen number of a self-map on an infra-nilmanifold. For the case of nilmanifolds this formula was extended to $n$-valued maps in [4]. In this paper, we extend these results further and establish the averaging formula to compute the Nielsen number of any $n$-valued affine map on an infra-nilmanifold.

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arXiv2026

Averaging formulas for the Reidemeister trace, Lefschetz and Nielsen numbers of $n$-valued maps

For an $n$-valued self-map $f$ of a closed manifold $X$, we prove an averaging formula for the Reidemeister trace of $f$ in terms of the Reidemeister coincidence traces of single-valued maps between finite orientable covering spaces of $X$. We then derive analogous formulas for the Lefschetz and Nielsen numbers of $f$. In the special case where $X$ is an infra-nilmanifold, we obtain explicit formulas for the Lefschetz and Nielsen numbers of any $n$-valued map on $X$.

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arXiv2026

Non-affine $n$-valued maps on tori

In this paper we construct $n$-valued maps on $k$-dimensional tori, where $n,k\geq 2$, that are not homotopic to affine $n$-valued maps. This is in high contrast with the single valued case, where any such map is homotopic to an affine (even linear) map. We do this by investigating necessary and sufficient algebraic conditions on certain induced morphisms.

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