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

@article{BronisławWajnryb2012,
abstract = {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.},
author = {Bronisław Wajnryb, Agnieszka Wiśniowska-Wajnryb},
journal = {Fundamenta Mathematicae},
keywords = {branched covering; Hurwitz action},
language = {eng},
number = {1},
pages = {1-11},
title = {Non-standard automorphisms of branched coverings of a disk and a sphere},
url = {http://eudml.org/doc/286503},
volume = {218},
year = {2012},
}

TY - JOUR
AU - Bronisław Wajnryb
AU - Agnieszka Wiśniowska-Wajnryb
TI - Non-standard automorphisms of branched coverings of a disk and a sphere
JO - Fundamenta Mathematicae
PY - 2012
VL - 218
IS - 1
SP - 1
EP - 11
AB - 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.
LA - eng
KW - branched covering; Hurwitz action
UR - http://eudml.org/doc/286503
ER -