English

Representing Dehn twists with branched coverings

Geometric Topology 2012-01-18 v6

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 B_n, with respect to a suitable branched covering p : F -> 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 x B^2.

Keywords

Cite

@article{arxiv.0710.0102,
  title  = {Representing Dehn twists with branched coverings},
  author = {Daniele Zuddas},
  journal= {arXiv preprint arXiv:0710.0102},
  year   = {2012}
}

Comments

Major revision. It has been added Corollary 3 about the lifting homomorphism. Are been added also some remarks and are given some other definitions. There are now 19 figures and 23 pages

R2 v1 2026-06-21T09:24:04.241Z