Rocky Mountain Journal of Mathematics

Hurwitz Spaces and Braid Group Representations

Eric P. Klassen and Yaacov Kopeliovich

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Rocky Mountain J. Math., Volume 34, Number 3 (2004), 1005-1030.

First available in Project Euclid: 5 June 2007

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Zentralblatt MATH identifier

Primary: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
Secondary: 20F36: Braid groups; Artin groups 20C12: Integral representations of infinite groups

Branched cover Hurwitz space braid group moduli space


Klassen, Eric P.; Kopeliovich, Yaacov. Hurwitz Spaces and Braid Group Representations. Rocky Mountain J. Math. 34 (2004), no. 3, 1005--1030. doi:10.1216/rmjm/1181069840.

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  • V.I. Arnol'd, Remark on the branching of hyperelliptic integrals as functions of the parameters, Funct. Anal. Appl. 2 (1968), 187-189.
  • Joan S. Birman, Braids, links, and mapping class groups, Ann. of Math. Stud., no. 82, Princeton Univ. Press, Princeton, 1974.
  • E. Faddell and J. Van Buskirk, The braid groups of $E^2$ and $S^2$, Duke Math. J. 29 (1962), 243-258.
  • Mike Fried, Fields of definition of function fields and Hurwitz families-Groups as Galois groups, Comm. Algebra 5 (1977), 17-82.
  • --------, Combinatorial computations of moduli dimension of Nielsen classes of covers, Contemp. Math., vol. 89, Amer. Math. Soc., Providence, 1989, pp. 61-79.
  • M. Fried, E. Klassen and Y. Kopeliovich, Realizing alternating groups as monodromy groups of genus one covers, Proc. Amer. Math. Soc. 129 (2000), 111-119.
  • M. Fried and H. Völklein, The inverse Galois problem and rational points on moduli spaces, Math. Ann. 290 (1991), 771-800.
  • R. Gillette and J. Van Buskirk, The word problem and its consequences for the braid groups and mapping class groups of the $2$-sphere, Trans. Amer. Math. Soc. 131 (1968), 277-296.
  • R. Guralnick and M. Neubauer, Monodromy groups of branched coverings: The generic case, in Recent developments in the inverse Galois problem, Contemp. Math., vol. 186, Amer. Math. Soc., Providence, 1995, pp. 325-352.
  • William E. Haver, Topological description of the space of homeomorphisms on closed $2$-manifolds, Illinois J. Math. 19 (1975), 632-635.
  • R. Kirby and L. Siebenmann, Foundational essays on topological manifolds, smoothings and triangulations, Ann. of Math. Stud., no. 88, Princeton Univ. Press, Princeton, 1977.
  • W. Magnus and A. Peluso, On a theorem of V.I. Arnol'd, Comm. Pure Appl. Math. 22 (1969), 683-692.
  • C.L. Tretkoff and M.D. Tretkoff, Combinatorial group theory, Riemann surfaces and differential equations, Contemp. Math., vol. 33, Amer. Math. Soc., Providence, 1984, pp. 467-519.
  • H. Völklien, Groups as Galois groups, Cambridge Stud. Adv. Math., vol. 53, Cambridge Univ. Press, Cambridge, 1996.
  • --------, Moduli spaces for covers of the Riemann sphere, Israel J. Math. 85 (1994), 407-430.