Bulletin of the Belgian Mathematical Society - Simon Stevin

The Nielsen Borsuk-Ulam number

Fabiana Santos Cotrim and Daniel Vendrúscolo

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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 $n\ge 3$.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 24, Number 4 (2017), 613-619.

First available in Project Euclid: 4 January 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55M20: Fixed points and coincidences [See also 54H25]

Borsuk-Ulam Theorem Nielsen theory Coincidence theory


Cotrim, Fabiana Santos; Vendrúscolo, Daniel. The Nielsen Borsuk-Ulam number. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 4, 613--619. doi:10.36045/bbms/1515035010. https://projecteuclid.org/euclid.bbms/1515035010

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