The Nielsen Borsuk-Ulam number
The paper under review is an extension of previous work of the authors on maps between finite dimensionsal complexes [Topology Appl. 159, No. 18, 3738--3745 (2012; Zbl 1260.55003)]. The authors introduce a Nielsen-Borsuk-Ulam number \(\mathrm{NBU}(f,\tau)\) for a continuous map \(f:X \to Y\), where \(X\) and \(Y\) are closed orientable triangulable \(n\)-manifolds and \(\tau\) is a free involution on \(X\). The number \(\mathrm{NBU}(f,\tau)\) shown to be a lower bound, in the homotopy class of \(f\), for the number of pairs of points in \(X\) satisfying \(f(x)=f(\tau(x))\). Further, it is proved that \(\mathrm{NBU}(f,\tau)\) can be realized (a Wecken type theorem) when \(n\geq3\).
scientific article; zbMATH DE number 6848704