| Texto completo | |
| Autor(es): |
Goncalves, D. L.
;
Gonzalez, J.
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | LOBACHEVSKII JOURNAL OF MATHEMATICS; v. 46, n. 3, p. 19-pg., 2025-03-01. |
| Resumo | |
For a finite group H and connected topological spaces X and Y such that X is endowed with a free left H-action tau, we provide a geometric condition in terms of the existence of a commutative diagram of spaces (arising from the triple (X, Y; tau)) to decide whether the Borsuk-Ulam property holds for based homotopy classes alpha is an element of[X, Y]0, as well as for free homotopy classes alpha is an element of[X, Y]. Here a homotopy class alpha is said to satisfy the Borsuk-Ulam property if, for each of its representatives f is an element of alpha, there exists an H-orbit, where f fails to be injective. Our geometric characterization is attained by constructing an H-equivariant map fromX to the classical configuration space F|H|(Y). We derive an algebraic condition from the geometric characterisation, and show that former one is in fact equivalent to the latter one whenX and Y are aspherical. We then specialize to the 1-dimensional case, i.e., whenX is an arbitrary connected graph, H is cyclic, and Y is either a tree, a circle, or the connected graph S1 boolean OR I with two vertices and two edges one of which is a loop and the other is a closed interval. The graph-braid-group ingredient in our characterizations is then effectively controlled through the use of discreteMorse theory. (AU) | |
| Processo FAPESP: | 22/16455-6 - Topologia algébrica, geométrica e diferencial |
| Beneficiário: | Daciberg Lima Gonçalves |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 16/24707-4 - Topologia algébrica, geométrica e diferencial |
| Beneficiário: | Daciberg Lima Gonçalves |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |