Isotopies of homeomorphisms of Riemann surfaces and a theorem about Artin's braid group

@article{Birman1972IsotopiesOH,
  title={Isotopies of homeomorphisms of Riemann surfaces and a theorem about Artin's braid group},
  author={Joan S. Birman and Hugh M. Hilden},
  journal={Annals of Mathematics},
  year={1972},
  volume={97},
  pages={424-439}
}
Let X, X be orientable surfaces. Let (p, X, X) be a regular covering space, possibly branched, with finitely many branch points and a finite group of covering transformations. We require also that every covering transformation leave the branch points fixed. A homeomorphism g : X -> X is said to be "fiber-preserving" with respect to the triplet (p,X,X) if for every pair of points x , x ' e l the condition p(x) = p(x') implies pg(x) = pg(x'). If g is fiber-preserving and isotopic to the identity… 
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References

SHOWING 1-10 OF 13 REFERENCES
Geometrical realization of isomorphisms between plane groups
az + b w = ; a, b, c, d real ad — be = — 1. cz + d We denote the upper half-plane by D, so that [G, D] is a transformation group with the topology on G and D induced by the parameters a, b, c, d, z.
Introduction to Riemann Surfaces
Introduction: 1-1 Algebraic functions and Riemann surfaces 1-2 Plane fluid flows 1-3 Fluid flows on surfaces 1-4 Regular potentials 1-5 Meromorphic functions 1-6 Function theory on a torus General
Die Klassen von topologischen Abbildungen einer geschlossenen Fläche auf sich
Die topologischen Abbildungen einer geschlossenen orientierbaren oder nichtorientierbaren Flache F auf sich zerfallen bekanntlich in Isotopieklassen. Zwei Abbildungen gehoren zu derselben
On the Mapping Class Group of Closed Surfaces as Covering Spaces
Theorie der Zöpfe
Über Automorphismen von Fundamentalgruppen berandeter Flächen
...
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