Lifting of homeomorphisms to branched coverings of a disk

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

Abstrakty

EN

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.

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: 217
• Numer: 2
• Strony: 95-122

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/fm217-2-1