We show that any homologically non-trivial Dehn twist of a compact surface $F$ with boundary is the lifting of a half-twist in the braid group ${cal B}_{n}$, with respect to a suitable branched covering $p : F o B^2$. In particular, we allow the surface to have disconnected boundary. As a consequence, any allowable Lefschetz fibration on $B^2$ is a branched covering of $B^2 imes B^2$.
Representing Dehn twists with branched coverings / Zuddas, D. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - STAMPA. - 2009:3(2009), pp. 387-413. [10.1093/imrn/rnn134]
Representing Dehn twists with branched coverings
ZUDDAS D
2009-01-01
Abstract
We show that any homologically non-trivial Dehn twist of a compact surface $F$ with boundary is the lifting of a half-twist in the braid group ${cal B}_{n}$, with respect to a suitable branched covering $p : F o B^2$. In particular, we allow the surface to have disconnected boundary. As a consequence, any allowable Lefschetz fibration on $B^2$ is a branched covering of $B^2 imes B^2$.File in questo prodotto:
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