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THE BORSUK-ULAM PROPERTY FOR HOMOTOPY CLASSES OF MAPS FROM THE TORUS TO THE KLEIN BOTTLE PART 2

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Autor(es):
Goncalves, Daciberg Lima ; Guaschi, John ; Laass, Vinicius Casteluber
Número total de Autores: 3
Tipo de documento: Artigo Científico
Fonte: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS; v. 60, n. 2, p. 26-pg., 2022-12-01.
Resumo

Let M be a topological space that admits a free involution r, and let N be a topological space. A homotopy class beta is an element of [M, N] is said to have the Borsuk-Ulam property with respect to r if for every representative map f : M -> N of beta, there exists a point x is an element of M such that f (r(x)) = f (x). In this paper, we determine the homotopy class of maps from the 2-torus T2 to the Klein bottle K2 that possess the Borsuk-Ulam property with respect to any free involution of T2 for which the orbit space is K2. Our results are given in terms of a certain family of homomorphisms involving the fundamental groups of T2 and K2. This completes the analysis of the Borsuk-Ulam problem for the case M = T2 and N = K2, and for any free involution r of T2. (AU)

Processo FAPESP: 16/24707-4 - Topologia algébrica, geométrica e diferencial
Beneficiário:Daciberg Lima Gonçalves
Modalidade de apoio: Auxílio à Pesquisa - Temático