On nonsymmetric theorems for $(H,G)$-coincidences

Abstract

Let $X$ be a compact Hausdorff space, $\varphi\colon X\to
S^{n}$ a continuous map into the $n$-sphere $S^n$ that induces a
nonzero homomorphism $\varphi^{*}\colon H^{n}(S^{n};{\mathbb Z}_{p})\to
H^{n}(X;{\mathbb Z}_{p})$, $Y$ a $k$-dimensional CW-complex and
$f\colon X\to Y$ a continuous map. Let $G$ a finite group which acts
freely on $S^{n}$. Suppose that $H\subset G$ is a normal cyclic
subgroup of a prime order. In this paper, we define and we estimate
the cohomological dimension of the set $A_{\varphi}(f,H,G)$ of
$(H,G)$-coincidence points of $f$ relative to $\varphi$.