# Erratum to `Isotopies of homeomorphisms of Riemann surfaces’

@article{Birman2017ErratumT, title={Erratum to `Isotopies of homeomorphisms of Riemann surfaces’}, author={Joan S. Birman and Hugh M. Hilden}, journal={Annals of Mathematics}, year={2017}, volume={185}, pages={345-345} }

There is an error in the statement and proof of Lemma 5.1 of [1]. The Lemma in question is true in some cases and false in others. The error does not affect the main body of [1], that is Theorems 1,2,3 and 4, but it does imply that Theorem 5, the proof of which uses Lemma 5.1, is true precisely when Lemma 5.1 is true and must be modified when it is false. Theorem 5 of [1] is well-known to be true in the case of hyperelliptic covering spaces of the punctured sphere. That application has been…

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We characterize the cyclic branched covers of the 2-sphere where every homeomorphism of the sphere lifts to a homeomorphism of the covering surface. This answers a question that appeared in an early…