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Relative Borsuk-Ulam Theorems for Spaces with a Free ℤ₂-action

Denise de Mattos; Thaís F. M. Monis; Edivaldo L. dos Santos — 2013

Bulletin of the Polish Academy of Sciences. Mathematics

Let (X,A) be a pair of topological spaces, T : X → 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 $f : X \to ℝ^{k}$ have a T-coincidence point, that is, a point x ∈ 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.

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