Coincidence theorems for maps of free \(\mathbb Z_p\)-spaces (Q411816)

Let \(f: X\to Y\) be a map, where \(X\) has a \(\mathbb Z_p\)-action. A point \(x_0\) is said to be a \(\mathbb Z_p\)-coincidence point if its \(\mathbb Z_p\)-action orbit has the same image under \(f\). The authors of this paper find some conditions to guarantee the existence of \(\mathbb Z_p\)-coincidence points for any map \(f: X\to Y\) when the \(\mathbb Z_p\)-action is free. Such a result can be regarded as a generalization of the Borsuk-Ulam theorem, where \(Y=\mathbb R^n\) and \(X=S^n\) with the natural \(\mathbb Z_2\)-action (the antipodal map).