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A Remark about Components of Relative Teichmüller Spaces

Published online by Cambridge University Press:  20 November 2018

Jane Gilman
Jane Gilman*
Affiliation:
Rutgers University Newark, New Jersey 07102 and The Institute for Advanced Study Princeton, New Jersey 08540
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Our aim is to compute for all n > 2, ψ(n, h), the number of components of a certain quotient of the fixed point set of an involution in the "mod-n" Teichmuller space. This answers part of a question raised by Earle [2] and corrects and extends the answer due to Zarrow (See Theorem 2 of [6]).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 2 , 01 June 1981 , pp. 245 - 246
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Earle, C. J. and Schatz, A., “Teichmuller theory for surfaces with boundary”, J. Diff. Geom., 4,. 2 (1971), 169-185.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 Univ. Press (1971), 119-130.Google Scholar
3. Gilman, J., “Compact Riemann surfaces with conformai involutions”, Proc. A.M.S., 37 (1973), 105-107.Google Scholar
4. Gilman, J., “On conjugacy classes in the Teichmuller modular group”, Mich. Math. J.,. 23 (1976), 53-63.Google Scholar
5. Gilman, J., “A matrix representation for automorphisms of compact Riemann surfaces”, Lin. Alg. and its Appl,. 17 (1977), 139-147.Google Scholar
6. Zarrow, R., “On Earle's mod n relative Teichmuller spaces”, Canad. Math. Bull,. 21 (1978), 355-360.Google Scholar