Non-standard automorphisms of branched coverings of a disk and a sphere

• Autorzy: Bronisław Wajnryb , Agnieszka Wiśniowska-Wajnryb
• Języki publikacji: EN

Abstrakty

EN

Let Y be a closed 2-dimensional disk or a 2-sphere. We consider a simple, d-sheeted branched covering π: X → Y. We fix a base point A₀ in Y (A₀ ∈ ∂Y if Y is a disk). We consider the homeomorphisms h of Y which fix ∂Y pointwise and lift to homeomorphisms ϕ of X-the automorphisms of π. We prove that if Y is a sphere then every such ϕ is isotopic by a fiber-preserving isotopy to an automorphism which fixes the fiber $π^{-1}(A₀)$ pointwise. If Y is a disk, we describe explicitly a small set of automorphisms of π which induce all allowable permutations of $π^{-1}(A₀)$. This complements our result in Fund. Math. 217 (2012), no. 2, where we found a set of generators for the group of isotopy classes of automorphisms of π which fix the fiber $π^{-1}(A₀)$ pointwise.

Kategorie tematyczne

• 57M12: Special coverings, e.g. branched
• 20F38: Other groups related to topology or analysis
• 20F36: Braid groups; Artin groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2012
• Tom: 218
• Numer: 1
• Strony: 1-11

Daty

wydano

2012

Twórcy

autor

Bronisław Wajnryb

• Department of Mathematics, Rzeszów University of Technology, Powstańców Warszawy 12, 35-959 Rzeszów, Poland

autor

Agnieszka Wiśniowska-Wajnryb

• Department of Mathematics, Rzeszów University of Technology, Powstańców Warszawy 12, 35-959 Rzeszów, Poland

Identyfikatory

DOI

10.4064/fm218-1-1