Relative Borsuk–Ulam Theorems for Spaces with a Free $\mathbb{Z}_2$-action
Volume 61 / 2013
Bulletin Polish Acad. Sci. Math. 61 (2013), 71-77
MSC: Primary 55M20; Secondary 55M35.
DOI: 10.4064/ba61-1-8
Abstract
Let $(X,A)$ be a pair of topological spaces, $T : X \to X$ a free involution and $A$ a $T$-invariant subset of $X$. In this context, a question that naturally arises is whether or not all continuous maps $f : X \to \mathbb{R}^{k}$ have a $T$-coincidence point, that is, a point $x \in X$ with $f (x) = f (T (x))$. In this paper, we obtain results of this nature under cohomological conditions on the spaces $A$ and $X$.
