Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T22:43:14.678Z Has data issue: false hasContentIssue false

On Earle's mod n Relative Teichmüller Spaces

Published online by Cambridge University Press:  20 November 2018

Robert Zarrow*
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, Dekalb, Illinois 60115
Rights & Permissions [Opens in a new window]

Extract

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.

In this paper we answer an open question of C. J. Earle ([2] §3.3 remarks (a) and (b)) in several cases. We first give some definitions and state some results which are given in greater detail in [2].

We let X be a smooth surface of genus g ≥ 2 and let M (X) be the space of smooth complex structures with the C topology. If μ∈M(X) let Xμ denote the Riemann surface determined by μ.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Ailing, N. L. and Greenleaf, N., Foundations of the theory of Klein surfaces, Lecture Notes in Math., vol. 219, Springer-Verlag, New York, 1971.Google Scholar
2. Earle, C. J., On the moduli of closed Riemann surfaces with symmetries, Advances in the Theory of Riemann surfaces, Ann. of Math, studies no. 66, Princeton University Press 1971, pp. 119-130.Google Scholar
3. Earle, C. J., A fact about matrices, preprint.Google Scholar
4. Gilman, J., A matrix representation for automorphisms of compact Riemann surfaces, Linear Algebra and its applications, 17 (1977), pp. 139-147.Google Scholar
5. Gilman, J., On conjugacy classes in the Teichmuller modular group, Mich. Math. J., 23 (1976), pp. 53-63.Google Scholar
6. Kato, Takao, Analytic self mappings inducing the identity on ), to appear.Google Scholar
7. Zarrow, R., A canonical form for symmetric and skew-symmetric extended symplectic modular matrices with applications to Riemann surface theory, Trans. Amer. Math. Soc, 204 (1975), pp.207-227.Google Scholar