# zbMATH — the first resource for mathematics

The Nielsen Borsuk-Ulam number. (English) Zbl 1386.55003
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 $$n\geq3$$.
##### MSC:
 55M20 Fixed points and coincidences in algebraic topology
##### Keywords:
Borsuk-Ulam theorem; Nielsen theory; coincidence theory
Full Text: