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## Lifting of homeomorphisms to branched coverings of a disk

### Tom 217 / 2012

Fundamenta Mathematicae 217 (2012), 95-122 MSC: Primary 20F36, 20F38, 57M12. DOI: 10.4064/fm217-2-1

#### Streszczenie

We consider a simple, possibly disconnected, $d$-sheeted branched covering $\pi$ 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 ${\bf B}_n$, 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 $L^\pi$ of finite index in ${\bf B}_n$. For each equivalence class of simple, $d$-sheeted coverings $\pi$ of $D$ with $n$ branch values we find an explicit small set generating $L^\pi$. The generators are powers of half-twists.

#### Autorzy

• Bronisław WajnrybDepartment of Mathematics
Rzeszów University of Technology
Powstańców Warszawy 12
35-959 Rzeszów, Poland
e-mail
• Agnieszka Wiśniowska-WajnrybDepartment of Mathematics
Rzeszów University of Technology
Powstańców Warszawy 12
35-959 Rzeszów, Poland
e-mail

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