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arXiv · 2107.02356

Nielsen-Borsuk-Ulam number for maps between tori

Givanildo Donizeti de Melo·Daniel Vendrúscolo
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Abstract

We compute the Nielsen-Borsuk-Ulam number for any selfmap of $n-$torus, $\mathbb{T}^n$, as well as any free involution $\tau$ in $\mathbb{T}^n$, with $n \leqslant 3$. Finally, we conclude that the tori, $\mathbb{T}^1$, $\mathbb{T}^2$ and $\mathbb{T}^3$, are Wecken spaces in Nielsen-Borsuk-Ulam theory. Such a number is a lower bound for the minimal number of pair of points such that $f(x)=f(\tau(x))$ in a given homotopy class of maps.

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BibTeXRIS

Givanildo Donizeti de Melo, Daniel Vendrúscolo. 2021-07-06. Nielsen-Borsuk-Ulam number for maps between tori. https://arxiv.org/abs/2107.02356

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