The balanced superelliptic mapping class groups are generated by three elements

References

[1] J. S. Birman, H. M. Hilden, On the mapping class groups of closed surfaces as covering spaces. In: Advances in the Theory of Riemann Surfaces(Proc. Conf., Stony Brook, N. Y., 1969), 81–115, Princeton Univ. Press 1971. MR292082 Zbl 0217.4860210.1515/9781400822492-007Search in Google Scholar

[2] J. S. Birman, H. M. Hilden, Lifting and projecting homeomorphisms. Arch. Math. (Basel) 23 (1972), 428–434. MR321071 Zbl 0247.5500110.1007/BF01304911Search in Google Scholar

[3] J. S. Birman, H. M. Hilden, On isotopies of homeomorphisms of Riemann surfaces. Ann. of Math. (2) 97 (1973), 424–439. MR325959 Zbl 0237.5700110.2307/1970830Search in Google Scholar

[4] M. Dehn, Die Gruppe der Abbildungsklassen. Acta Math. 69 (1938), 135–206. MR1555438 Zbl 0019.2530110.1007/BF02547712Search in Google Scholar

[5] B. Farb, D. Margalit, A primer on mapping class groups. Princeton Univ. Press 2012. MR2850125 Zbl 1245.5700210.1515/9781400839049Search in Google Scholar

[6] S. Gervais, A finite presentation of the mapping class group of a punctured surface. Topology 40 (2001), 703–725. MR1851559 Zbl 0992.5701310.1016/S0040-9383(99)00079-8Search in Google Scholar

[7] T. Ghaswala, R. R. Winarski, The liftable mapping class group of balanced superelliptic covers. New York J. Math. 23 (2017), 133–164. MR3611078 Zbl 1402.57003 Compare the revised version from 2019 under arXiv:1604.03908Search in Google Scholar

[8] T. Ghaswala, R. R. Winarski, Lifting homeomorphisms and cyclic branched covers of spheres. Michigan Math. J. 66 (2017), 885–890. MR3720329 Zbl 1383.5700110.1307/mmj/1508810819Search in Google Scholar

[9] S. Hirose, G. Omori, Finite presentations for the balanced superelliptic mapping class groups. Preprint 2022, arXiv:2203.13413Search in Google Scholar

[10] S. P. Humphries, Generators for the mapping class group. In: Topology of low-dimensional manifolds(Proc. Second Sussex Conf., Chelwood Gate, 1977), volume 722 of Lecture Notes in Math., 44–47, Springer 1979. MR547453 Zbl 0732.5700410.1007/BFb0063188Search in Google Scholar

[11] M. Korkmaz, Generating the surface mapping class group by two elements. Trans. Amer. Math. Soc. 357 (2005), 3299–3310. MR2135748 Zbl 1079.5701810.1090/S0002-9947-04-03605-0Search in Google Scholar

[12] C. Labruère, L. Paris, Presentations for the punctured mapping class groups in terms of Artin groups. Algebr. Geom. Topol. 1 (2001), 73–114. MR1805936 Zbl 0962.5700810.2140/agt.2001.1.73Search in Google Scholar

[13] W. B. R. Lickorish, A finite set of generators for the homeotopy group of a 2-manifold. Proc. Cambridge Philos. Soc. 60 (1964), 769–778. MR171269 Zbl 0131.2080110.1017/S030500410003824XSearch in Google Scholar

[14] N. Monden, On minimal generating sets for the mapping class group of a punctured surface. Preprint 2021, arXiv:2103.01525Search in Google Scholar

[15] M. Stukow, Small torsion generating sets for hyperelliptic mapping class groups. Topology Appl. 145 (2004), 83–90. MR2100866 Zbl 1069.5700910.1016/j.topol.2004.06.004Search in Google Scholar

[16] B. Wajnryb, Mapping class group of a surface is generated by two elements. Topology 35 (1996), 377–383. MR1380505 Zbl 0860.5704010.1016/0040-9383(95)00037-2Search in Google Scholar