The Borsuk-Ulam property for homotopy classes of maps between the torus and the Klein bottle
Résumé
Let M be a topological space that admits a free involution τ , and let N be a topological space. A homotopy class β ∈ [M, N] is said to have the Borsuk-Ulam property with respect to τ if for every representative map f : M → N of β, there exists a point x ∈ M such that f (τ (x)) = f (x). In this paper, we determine the homotopy classes of maps from the 2-torus T^2 to the Klein bottle K^2 that possess the Borsuk-Ulam property with respect to a free involution τ_1 of T^2 for which the orbit space is T^2. Our results are given in terms of a certain family of homomorphisms involving the fundamental groups of T^2 and K^2 .
Domaines
Topologie géométrique [math.GT]
Origine : Fichiers produits par l'(les) auteur(s)
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