Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-06-06T14:29:09.439Z Has data issue: false hasContentIssue false
  • English
  • Français

The Eichler Trace of ℤp Actions on Riemann Surfaces

Published online by Cambridge University Press:  20 November 2018

Denis Sjerve  and
Qing Jie Yang
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study ${{\mathbb{Z}}_{p}}$ actions on compact connected Riemann surfaces via their associated Eichler traces.We determine the set of possible Eichler traces and determine the relationship between 2 actions if they have the same trace.

Keywords

30F3057M60
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 3 , 01 June 1998 , pp. 620 - 637
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Carlitz, and Olson, , Maillet's Determinant. Proc. Amer.Math. Soc. 6(1955), 265–269.Google Scholar
2. Eckmann, and Müeller, , Plane Motion Groups and Virtual Poincaré Duality in Dimension Two. Invent. Math. 69(1982), 293–310.Google Scholar
3. Edmonds, and Ewing, , Remarks on the cobordism group of Surface diffeomorphisms. Math. Ann. 259(1982), 497–504.Google Scholar
4. Edmonds, and Ewing, , Surface Symmetry and Homology. Math. Proc. Cambridge Philos. Soc. 99(1986), 73–77.Google Scholar
5. Ewing, , The Image of the Atiyah-Bott Map. Math. Z. 165(1979), 53-71.Google Scholar
6. Ewing, , Automorphisms of Surfaces and Class Numbers: An Illustration of the G-Index Theorem. In: Topological Topics, (ed., James, I.M.), London Math. Soc. Lecture Notes Serie. 86, Cambridge Univ. Press,1983, 120–127.Google Scholar
7. Farkas, and Kra, , Riemann Surfaces. Graduate Texts in Math. 71, Springer-Verlag, 1980.Google Scholar
8. Gabai, , Convergence Groups are Fuchsian. Ann. of Math. 136(1992), 447–510.Google Scholar
9. Kerckhoff, , The Nielsen Realization Problem. Ann. of Math. 117(1983), 235–265.Google Scholar
10. Lang, , Cyclotomic Fields I and II. Springer-Verlag, New York, 1990.Google Scholar
11. Nielsen, , Die Struktur periodischer Transformationen von Flächen. Mat.-Fys. Medd. Danske Vid. Selsk. 15(1937), 1–77.Google Scholar
12. Nielsen, , Abbildungsklassen endlicher Ordnung. Acta Math. 75(1942), 23–115.Google Scholar
13. Symonds, , The Cohomology Representation of an action of ℤ p on a surface. Trans. Amer. Math. Soc. 306(1988), 389–400.Google Scholar