Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

CONJUGACY CLASSES OF AUTOMORPHISMS p-GROUPS

  • Hidalgo, Ruben A. (Departamento de Matematica Universidad Tecnica Federico Santa Maria)
  • Received : 2010.01.13
  • Published : 2011.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we provide examples of pairs of conformally non-equivalent, but topologically equivalent, p-groups $H_1$, $H_2$ < Aut(S), where S is a closed Riemann surface of genus g ${\geq}$ 2, so that $S/H_j$ has genus zero and all its cone points are of order equal to p.

Keywords

References

  1. A. Carocca, V. Gonzalez-Aguilera, R. A. Hidalgo, and R. E. Rodriguez, Generalized Humbert curves, Israel J. Math. 164 (2008), 165-192. https://doi.org/10.1007/s11856-008-0025-2
  2. M. Carvacho, Equivalence of Actions on Compact Riemann Surfaces, Ph. D. Thesis. U. de Chile, 2010.
  3. G. Castelnuovo, Sulle serie algebriche di gruppi di punti appartenenti ad una curve algebraica, Rendiconti della R. Academia dei Lincei Series 5, XV, 1906 (Memorie scelte p. 509)
  4. G. Gonzalez-Diez, On prime Galois coverings of the Riemann sphere, Ann. Mat. Pura Appl. (4) 168 (1995), 1-15. https://doi.org/10.1007/BF01759251
  5. G. Gonzalez-Diez, Loci of curves which are prime Galois coverings of $P^1$, Proc. London Math. Soc. (3) 62 (1991), no. 3, 469-489. https://doi.org/10.1112/plms/s3-62.3.469
  6. G. Gonzalez-Diez and W. J. Harvey, Moduli of Riemann surfaces with symmetry, Discrete groups and geometry (Birmingham, 1991), 75-93, London Math. Soc. Lecture Note Ser., 173, Cambridge Univ. Press, Cambridge, 1992.
  7. G. Gonzalez-Diez and R. A. Hidalgo, Conformal versus topological conjugacy of automorphisms on compact Riemann surfaces, Bull. London Math. Soc. 29 (1997), no. 3, 280-284. https://doi.org/10.1112/S0024609396002640
  8. G. Gonzalez-Diez, R. A. Hidalgo, and M. Leyton, Generalized Fermat curves, J. Algebra 321 (2009), no. 6, 1643-1660. https://doi.org/10.1016/j.jalgebra.2009.01.002
  9. J. Gilman, On conjugacy classes in the Teichmuller modular group, Michigan Math. J. 23 (1976), no. 1, 53-63. https://doi.org/10.1307/mmj/1029001621
  10. G. Gromadzki, On conjugacy of p-gonal automorphisms of Riemann surfaces, Rev. Mat. Complut. 21 (2008), no. 1, 83-87.
  11. G. Gromadzki, A. Weaver, and A. Wootton, On gonality of Riemann surfaces, Geometriae Dedicata 149 (2010), No. 1, 1-14. https://doi.org/10.1007/s10711-010-9459-x
  12. W. J. Harvey, On branch loci in Teichmuller space, Trans. Amer. Math. Soc. 153 (1971), 387-399.
  13. M. Leyton and R. A. Hidalgo, On uniqueness of automorphisms groups of Riemann surfaces, Rev. Mat. Iberoam. 23 (2007), no. 3, 793-810.
  14. J. Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flachen, Acta Math. 50 (1927), 189-358. https://doi.org/10.1007/BF02421324
  15. W. P. Thurston, The geometry and topology of 3-manifolds, Princeton Lecture Notes (1978-1981).