The Michigan Mathematical Journal

Lifting Homeomorphisms and Cyclic Branched Covers of Spheres

Tyrone Ghaswala and Rebecca R. Winarski

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Abstract

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 the question that appeared in an early version of the erratum of Birman and Hilden [2].

Article information

Source
Michigan Math. J., Volume 66, Issue 4 (2017), 885-890.

Dates
Received: 3 August 2016
Revised: 1 December 2016
First available in Project Euclid: 24 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1508810819

Digital Object Identifier
doi:10.1307/mmj/1508810819

Mathematical Reviews number (MathSciNet)
MR3720329

Zentralblatt MATH identifier
06822191

Subjects
Primary: 57M12: Special coverings, e.g. branched
Secondary: 57M60: Group actions in low dimensions

Citation

Ghaswala, Tyrone; Winarski, Rebecca R. Lifting Homeomorphisms and Cyclic Branched Covers of Spheres. Michigan Math. J. 66 (2017), no. 4, 885--890. doi:10.1307/mmj/1508810819. https://projecteuclid.org/euclid.mmj/1508810819


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References

  • [1] J. S. Birman and H. M. Hilden,On isotopies of homeomorphisms of Riemann surfaces, Ann. of Math. (2) 97 (1973), 424–439.
  • [2] J. S. Birman and H. M. Hilden,Erratum to ‘Isotopies of homeomorphisms of Riemann surfaces’, Ann. of Math. (2) 185 (2017), no. 1, 345.
  • [3] T. Brendle, D. Margalit, and A. Putman,Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at $t=-1$, Invent. Math. 200 (2015), no. 1, 263–310.
  • [4] S. Gorchinskiy and F. Viviani,Picard group of moduli of hyperelliptic curves, Math. Z. 258 (2008), no. 2, 319–331.
  • [5] R. A. Hidalgo,Schottky double covers, Rev. Mat. Complut. 23 (2010), no. 1, 37–48.
  • [6] C. Johnson and M. Schmoll,Hyperelliptic translation surfaces and folded tori, Topology Appl. 161 (2014), 73–94.
  • [7] T. Morifuji,On Meyer’s function of hyperelliptic mapping class groups, J. Math. Soc. Japan 55 (2003), no. 1, 117–129.
  • [8] J. C. Rohde,Cyclic coverings, Calabi–Yau manifolds and complex multiplication, Lecture Notes in Math., 1975, Springer-Verlag, Berlin, 2009.