| Texto completo | |
| Autor(es): |
Cadavid-Aguilar, Nataliay
;
Gonzalez, Jesus
;
Gutierrez, Barbara
;
Ipanaque-Zapata, Cesar A.
Número total de Autores: 4
|
| Tipo de documento: | Artigo Científico |
| Fonte: | JOURNAL OF TOPOLOGY AND ANALYSIS; v. 16, n. 01, p. 18-pg., 2024-02-01. |
| Resumo | |
We introduce the effectual topological complexity (ETC) of a G-space X. This is a G-equivariant homotopy invariant sitting in between the effective topological complexity of the pair (X,G) and the (regular) topological complexity of the orbit space X/G. We study ETC for spheres and surfaces with antipodal involution, obtaining a full computation in the case of the torus. This allows us to prove the vanishing of twice the nontrivial obstruction responsible for the fact that the topological complexity of the Klein bottle is 4. In addition, this gives a counterexample to the possibility - suggested in Pave & scaron;i & cacute;'s work on the topological complexity of a map - that ETC of (X,G) would agree with Farber's TC(X) whenever the projection map X -> X/G is finitely sheeted. We conjecture that ETC of spheres with antipodal action recasts the Hopf invariant one problem, and describe (conjecturally optimal) effectual motion planners. (AU) | |
| Processo FAPESP: | 16/18714-8 - Espaços de configurações no problema de planificação de movimento simultâneo livre de colisões |
| Beneficiário: | Cesar Augusto Ipanaque Zapata |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |