Lifting of homeomorphisms to branched coverings of a disk

Bronisław Wajnryb, and Agnieszka Wiśniowska-Wajnryb. "Lifting of homeomorphisms to branched coverings of a disk." Fundamenta Mathematicae 217.2 (2012): 95-122. <http://eudml.org/doc/282872>.

@article{BronisławWajnryb2012,
abstract = {We consider a simple, possibly disconnected, d-sheeted branched covering π of a closed 2-dimensional disk D by a surface X. The isotopy classes of homeomorphisms of D which are pointwise fixed on the boundary of D and permute the branch values, form the braid group Bₙ, where n is the number of branch values. Some of these homeomorphisms can be lifted to homeomorphisms of X which fix pointwise the fiber over the base point. They form a subgroup $L^π$ of finite index in Bₙ. For each equivalence class of simple, d-sheeted coverings π of D with n branch values we find an explicit small set generating $L^π$. The generators are powers of half-twists.},
author = {Bronisław Wajnryb, Agnieszka Wiśniowska-Wajnryb},
journal = {Fundamenta Mathematicae},
keywords = {braid groups; generating sets; simple branched coverings; lifting of homeomorphisms},
language = {eng},
number = {2},
pages = {95-122},
title = {Lifting of homeomorphisms to branched coverings of a disk},
url = {http://eudml.org/doc/282872},
volume = {217},
year = {2012},
}

TY - JOUR
AU - Bronisław Wajnryb
AU - Agnieszka Wiśniowska-Wajnryb
TI - Lifting of homeomorphisms to branched coverings of a disk
JO - Fundamenta Mathematicae
PY - 2012
VL - 217
IS - 2
SP - 95
EP - 122
AB - We consider a simple, possibly disconnected, d-sheeted branched covering π of a closed 2-dimensional disk D by a surface X. The isotopy classes of homeomorphisms of D which are pointwise fixed on the boundary of D and permute the branch values, form the braid group Bₙ, where n is the number of branch values. Some of these homeomorphisms can be lifted to homeomorphisms of X which fix pointwise the fiber over the base point. They form a subgroup $L^π$ of finite index in Bₙ. For each equivalence class of simple, d-sheeted coverings π of D with n branch values we find an explicit small set generating $L^π$. The generators are powers of half-twists.
LA - eng
KW - braid groups; generating sets; simple branched coverings; lifting of homeomorphisms
UR - http://eudml.org/doc/282872
ER -