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december 2017 The Nielsen Borsuk-Ulam number
Fabiana Santos Cotrim, Daniel Vendrúscolo
Bull. Belg. Math. Soc. Simon Stevin 24(4): 613-619 (december 2017). DOI: 10.36045/bbms/1515035010

Abstract

A Nielsen-Borsuk-Ulam number ($NBU(f,\tau)$) is defined for continuous maps $f:X\to Y$ where $X$ and $Y$ are closed orientable triangulable $n$-mani\-folds and $X$ has a free involution $\tau$. This number is a lower bound, in the homotopy class of $f$, for the number of pairs of points in $X$ satisfying $f(x)=f\circ\tau(x)$. It is proved that $NBU(f,\tau)$ can be realized (Wecken type theorem) when $n\ge 3$.

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Fabiana Santos Cotrim. Daniel Vendrúscolo. "The Nielsen Borsuk-Ulam number." Bull. Belg. Math. Soc. Simon Stevin 24 (4) 613 - 619, december 2017. https://doi.org/10.36045/bbms/1515035010

Information

Published: december 2017
First available in Project Euclid: 4 January 2018

zbMATH: 06848704
MathSciNet: MR3743265
Digital Object Identifier: 10.36045/bbms/1515035010

Subjects:
Primary: ‎55M20

Rights: Copyright © 2017 The Belgian Mathematical Society

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Vol.24 • No. 4 • december 2017
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