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Erratum to ‘Isotopies of homeomorphisms of Riemann surfaces’. (English) Zbl 1420.57053

Erratum to the authors’ paper [ibid. 97, 424–439 (1973; Zbl 0237.57001)].
From the text: “There is an error in the statement and proof of Lemma 5.1 of [loc. cit.]. The lemma in question is true in some cases and false in others. The error does not affect the main body of [loc. cit.], 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 [loc. cit.] is well known to be true in the case of hyperelliptic covering spaces of the punctured sphere. Since [loc. cit.] was published 43 years ago and has been used by many authors, we checked through the 42 papers that, according to MathSciNet, cited our work, and verified that they had all used Theorems 1-4 but not Theorem 5.”
In [Mich. Math. J. 66, No. 4, 885–890 (2017; Zbl 1383.57001)], T. Ghaswala and R. R. Winarski give necessary and sufficient conditions for Lemma 5.1 to hold and give a concrete example where they fail to hold.

MSC:

57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
57M10 Covering spaces and low-dimensional topology
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References:

[1] J. S. Birman and H. M. Hilden, ”On isotopies of homeomorphisms of Riemann surfaces,” Ann. of Math., vol. 97, pp. 424-439, 1973. · Zbl 0237.57001
[2] T. Ghaswala and R. Winarski, Lifting homeomorphisms and cyclic branched covers of spheres. · Zbl 1402.57003
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