Bulletin of the Belgian Mathematical Society - Simon Stevin

The Nielsen Borsuk-Ulam number

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 $n\ge 3$.

Article information

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

Dates
First available in Project Euclid: 4 January 2018

https://projecteuclid.org/euclid.bbms/1515035010

Digital Object Identifier
doi:10.36045/bbms/1515035010

Mathematical Reviews number (MathSciNet)
MR3743265

Zentralblatt MATH identifier
06848704

Subjects