The invariant differential forms on the Teichmüller space under the Fenchel-Nielsen flows

Nariya KAWAZUMI

doi:10.2969/jmsj/04420217

Nariya KAWAZUMI

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JOURNAL FREE ACCESS

1992 Volume 44 Issue 2 Pages 217-237

DOI https://doi.org/10.2969/jmsj/04420217

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Published: 1992 Received: December 28, 1990 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: DTRECEIVED Details: Wrong : 19901028
Right : 19901228

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : Ab) W. Abikoff, The real analytic theory of Teichmüller space, Lecture Note in Math., 820, Springer-Verlag, Berlin-Heidelberg, 1976.
Ah) L. V. Ahlfors, Some remarks on Teichmüller's space of Riemann surfaces, Ann. of Math., 74 (1961), 171-191.
B) A. Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup., (4), 7 (1974), 235-272.
G1) W.M. Goldman, The symplectic nature of fundamental groups of surfaces, Adv. Math., 54 (1984), 200-225.
G2) W.M. Goldman, Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math., 85 (1986), 263-302.
H) J. L. Harer, The second homology group of the mapping class group of an orientable surface, Invent. Math., 72 (1983), 221-239.
K) S.P. Kerckhoff, The Nielsen realization problem, Ann. of Math., 117 (1983), 235-265.
L) W. B. R. Lickorish, A representation of orientable combinatorial 3-manifolds, Ann. of Math., 76 (1962), 531-540.
Ma) Y. Matsushima, On Betti numbers of compact, locally symmetric Riemannian manifolds, Osaka Math. J., 14 (1962), 1-20.
Mi) E. Y. Miller, The homology of the mapping class group, J. Differential Geom., 24 (1986), 1-14.
Mo) S. Morita, Characteristic classes of surface bundles, Invent. Math., 90 (1987), 551-577,
P) J. Powell, Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc., 68 (1978), 347-350.
W1) S. Wolpert, The Fenchel-Nielsen deformation, Ann. of Math., 115 (1982), 501-528.
W2) S. Wolpert,On the symplectic geometry of deformations of a hyperbolic surface, Ann. of Math., 117 (1983), 207-234.
W3) S. Wolpert, On the Weil-Petersson geometry of the moduli space of curves, Amer. J. Math., 107 (1985), 969-997.
W4) S. Wolpert, Geodesic length functions and the Nielsen problem, J. Differential Geom., 25 (1987), 275-296.

Right : [Ab] W. Abikoff, The real analytic theory of Teichmüller space, Lecture Note in Math., 820, Springer-Verlag, Berlin-Heidelberg, 1976.
[Ah] L. V. Ahlfors, Some remarks on Teichmüller's space of Riemann surfaces, Ann. of Math., 74 (1961), 171-191.
[B] A. Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup., (4), 7 (1974), 235-272.
[G1] W. M. Goldman, The symplectic nature of fundamental groups of surfaces, Adv. Math., 54 (1984), 200-225.
[G2] W. M. Goldman, Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math., 85 (1986), 263-302.
[H] J. L. Harer, The second homology group of the mapping class group of an orientable surface, Invent. Math., 72 (1983), 221-239.
[K] S. P. Kerckhoff, The Nielsen realization problem, Ann. of Math., 117 (1983), 235-265.
[L] W. B. R. Lickorish, A representation of orientable combinatorial 3-manifolds, Ann. of Math., 76 (1962), 531-540.
[Ma] Y. Matsushima, On Betti numbers of compact, locally symmetric Riemannian manifolds, Osaka Math. J., 14 (1962), 1-20.
[Mi] E. Y. Miller, The homology of the mapping class group, J. Differential Geom., 24 (1986), 1-14.
[Mo] S. Morita, Characteristic classes of surface bundles, Invent. Math., 90 (1987), 551-577,
[P] J. Powell, Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc., 68 (1978), 347-350.
[W1] S. Wolpert, The Fenchel-Nielsen deformation, Ann. of Math., 115 (1982), 501-528.
[W2] S. Wolpert,On the symplectic geometry of deformations of a hyperbolic surface, Ann. of Math., 117 (1983), 207-234.
[W3] S. Wolpert, On the Weil-Petersson geometry of the moduli space of curves, Amer. J. Math., 107 (1985), 969-997.
[W4] S. Wolpert, Geodesic length functions and the Nielsen problem, J. Differential Geom., 25 (1987), 275-296.

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