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On the homeotopy groups of surfaces. (English) Zbl 0248.55001


MSC:

57M05 Fundamental group, presentations, free differential calculus
57M10 Covering spaces and low-dimensional topology
57M20 Two-dimensional complexes (manifolds) (MSC2010)
30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
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References:

[1] Ahlfors, L.: On quasiconformal mappings. J. d’Analyse Math.3, 1-58 (1953/54) · Zbl 0057.06506 · doi:10.1007/BF02803585
[2] Baer, R.: Isotopie von Kurven auf orientierbaren, geschlossenen Flächen. J. reine angew. Math.159, 101-116 (1928) · JFM 54.0602.05 · doi:10.1515/crll.1928.159.101
[3] Birman, J. S., Hilden, M. H.: Lifting and projecting homeomorphisms. Archiv. Math.23, 428-434 (1972) · Zbl 0247.55001 · doi:10.1007/BF01304911
[4] Birman, J. S., Hilden, M. H.: On isotopies of homeomorphisms of Riemann surfaces, and a theorem about Artin’s braid groups. Ann. Math. (to appear) · Zbl 0255.57002
[5] Coldewey, H.-D.: Kanonische Polygone endlich erzeugter Fuchsscher Gruppen. Dissertation, Ruhr-Universität Bochum 1971
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[7] Keen, L.: On Fricke moduli. Advances in the theory of Riemann surfaces. Ann. Math. Studies 66. Princeton: Princeton Univ. Press 1971 · Zbl 0237.32013
[8] Macbeath, A. M.: Geometrical realisations of isomorphisms between plane groups. Bull. Amer. Math. Soc.71, 629-630 (1965) · Zbl 0137.40102 · doi:10.1090/S0002-9904-1965-11368-4
[9] Maclachlan, C., Harvey, W. J.: On mapping-class groups and Teichmüller spaces. (Preprint 1972) · Zbl 0303.32020
[10] Marden, A.: On homotopic mappings of Riemann surfaces. Ann. Math.90, 1-8 (1969) · Zbl 0214.08903 · doi:10.2307/1970677
[11] Tukia, P.: On discrete groups of the unit disc and their isomorphisms. Annales Acad. Sci. Fennicae I.504, 1-45 (1972) · Zbl 0225.30022
[12] Zieschang, H.: Diskrete Gruppen von Bewegungen der Ebene und ebene Gruppenbilder. Uspechi Mat. Nauk21 No 3, 195-212 (1966) · Zbl 0248.20066
[13] Zieschang, H.: Lifting and projecting homeomorphisms. Archiv Math. (to appear) · Zbl 0267.55002
[14] Zieschang, H., Vogt, E., Coldewey, H.-D.: Flächen und ebene diskontinuierliche Gruppen. Lecture Notes in Mathematics 122. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0204.24002
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