Abstract
Let ρ : F → D be a simple 3-sheeted branched covering of a 2-disc D, with an even number of branch values. Let L be the group of isotopy classes of liftable orientation-preserving homeomorphisms of D rel ∂D. Then lifting induces a homomorphism λ from L to the mapping class group of F. In this paper we prove that λ is surjective, and find a simple set of generators for L and two elements of L whose normal closure in L is kernel λ. Thus the mapping class group of F is exhibited as a quotient group of the group L, which is a subgroup of finite index in Artin's braid group.
This work was initiated when the first author visited Technion, Haifa, Israel. The partial support of the Lady Davis foundation for that visit is gratefully acknowledged. The work was also partially supported by the US National Science Foundation Grant MCS79-04715.
Partially supported by the Technion VPR Fund/The K. and M. Bank Fund.
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© 1985 Springer-Verlag
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Birman, J.S., Wajnryb, B. (1985). 3-fold branched coverings and the mapping class group of a surface. In: Geometry and Topology. Lecture Notes in Mathematics, vol 1167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075214
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DOI: https://doi.org/10.1007/BFb0075214
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