English

Nielsen-Borsuk-Ulam number for maps between tori

Algebraic Topology 2022-01-03 v2

Abstract

We compute the Nielsen-Borsuk-Ulam number for any selfmap of nn-torus, Tn\mathbb{T}^n, as well as any free involution τ\tau in Tn\mathbb{T}^n, with n3n \leqslant 3. Finally, we conclude that the tori, T1\mathbb{T}^1, T2\mathbb{T}^2 and T3\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(τ(x))f(x)=f(\tau(x)) in a given homotopy class of maps.

Keywords

Cite

@article{arxiv.2107.02356,
  title  = {Nielsen-Borsuk-Ulam number for maps between tori},
  author = {Givanildo Donizeti de Melo and Daniel Vendrúscolo},
  journal= {arXiv preprint arXiv:2107.02356},
  year   = {2022}
}

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21 pages