On branched covers of the $2$-sphere by the $2$-sphere
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- by S. M. Gersten PDF
- Proc. Amer. Math. Soc. 101 (1987), 761-766 Request permission
Abstract:
A new solution of the Hurwitz problem is given for realizing branch data by a branched cover of ${S^2}$ by ${S^2}$. The solution involves products of conjugacy classes in a free group.References
- Allan L. Edmonds, Ravi S. Kulkarni, and Robert E. Stong, Realizability of branched coverings of surfaces, Trans. Amer. Math. Soc. 282 (1984), no. 2, 773–790. MR 732119, DOI 10.1090/S0002-9947-1984-0732119-5
- S. M. Gersten, Products of conjugacy classes in a free group: a counterexample, Math. Z. 192 (1986), no. 2, 167–181. MR 840821, DOI 10.1007/BF01179420
- A. Hurwitz, Ueber Riemann’sche Flächen mit gegebenen Verzweigungspunkten, Math. Ann. 39 (1891), no. 1, 1–60 (German). MR 1510692, DOI 10.1007/BF01199469
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 761-766
- MSC: Primary 57M12
- DOI: https://doi.org/10.1090/S0002-9939-1987-0911047-4
- MathSciNet review: 911047