On Birman-Hilden theory and the relation between mapping class groups and braid groups:
Tyrone Ghaswala, Rebecca R. Winarski: Lifting Homeomorphisms and Cyclic Branched Covers of Spheres, Michigan Math. J. 66 4 (2017) 885-890 [arXiv:1607.06060, doi:10.1307/mmj/1508810819]
Dan Margalit, Rebecca R. Winarski: The Birman-Hilden theory, Celebratio Mathematics (Jan 2017) [arXiv:1703.03448, celebratio:471]
Dan Margalit, Rebecca R. Winarski: Braid groups and mapping class groups: The Birman–Hilden theory, Bull. London Math. Soc. 53 3 (2021) 643-659 [doi:10.1112/blms.12456]
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