Nielsen-Borsuk-Ulam number for maps between tori

2021/07/06 by de Melo, Givanildo Donizeti, Vendrúscolo, Daniel
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.02356

Abstract

We compute the Nielsen-Borsuk-Ulam number for any selfmap of n-torus, \mathbbTⁿ, as well as any free involution τ in \mathbbTⁿ, with n \leqslant 3. Finally, we conclude that the tori, \mathbbT¹, \mathbbT² and \mathbbT³, 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)) in a given homotopy class of maps.

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