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On Earle's mod n Relative Teichmüller Spaces

Published online by Cambridge University Press:  20 November 2018

Robert Zarrow
Robert Zarrow*
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, Dekalb, Illinois 60115
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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
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 3 , 01 September 1978 , pp. 355 - 360
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