Higher topological complexity of a map

Autor(es)

Ipanaque Zapata, Cesar A. ; Gonzalez, Jesus

• Tipo de documento: Artigo Científico
• Fonte: TURKISH JOURNAL OF MATHEMATICS; v. 47, n. 6, p. 28-pg., 2023-01-01.

Resumo

The higher topological complexity of a space X, TCr(X), r = 2, 3, ... , and the topological complexity of a map f , TC(f), have been introduced by Rudyak and Pavesic, respectively, as natural extensions of Farber's topological complexity of a space. In this paper we introduce a notion of higher topological complexity of a map f, TCr,s(f), for 1 <= s <= r >= 2, which simultaneously extends Rudyak's and Pavesic's notions. Our unified concept is relevant in the r -multitasking motion planning problem associated to a robot devise when the forward kinematics map plays a role in s prescribed stages of the motion task. We study the homotopy invariance and the behavior of TC(r,s )under products and compositions of maps, as well as the dependence of TCr,s on r and s. We draw general estimates for TCr,s(f : X -> Y ) in terms of categorical invariants associated to X, Y and f . In particular, we describe within one the value of TCr,s in the case of the nontrivial double covering over real projective spaces, as well as for their complex counterparts. (AU)

• Processo FAPESP: 22/03270-8 - Tranças, Espaços de configuração e aplicações em funções a valores múltiplos
• Beneficiário: Cesar Augusto Ipanaque Zapata
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• 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