This is a preview of subscription content, log in via an institution to check access.
References
[A] Ash, A.: Deformation retracts with lowest possible dimension of arithmetic quotients of self-adjoint homogeneous cones. Maht. Ann.225, 69–76 (1977)
[BE] Bieri, R., Eckmann, B.: Groups with homological duality generalizing Poincaré duality. Invent. Math.20, 103–124 (1973)
[BiS] Birman, J., Series, C.: An algorithm for simple curves on surfaces (Preprint 1983)
[B] Brown, K.: Cohomology of Groups. Graduate Tests in Mathematics, no. 87. Berlin-Heidelberg-New York: Springer 1982
[BS] Borel, A., Serre, J.-P.: Corners and arithmetic groups. Comment. Math. Helv.48, 436–491 (1973)
[CL] Charney, R., Lee, R.: Moduli space of stable curves from a homotopy viewpoint. (Preprint 1983)
[D] Diaz, S.: A bound on the dimension of complete subvarieties ofM g. (Preprint 1983)
[EG] Eilenberg, S., Ganea, T.: On the Lusternik-Schnirelmann category of abstract groups. Ann. Math.65, 517–518 (1957)
[H1] Harer, J.: The second homology group of the mapping class groups of orientable surfaces. Invent. Math.72, 221–239 (1983)
[H2] Harer, J.: Stability of the homology of the mapping class groups of orientable surfaces. (To appear in Ann. Math.)
[HM] Harris, J., Mumford, D.: On the Kodaira dimension of the moduli space of curves. Invent. Math.67, 23–86 (1982)
[Har] Harvey, W.: Boundary structure for the modular group. Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference. Ann. Math. Stud.97, 245–251 (1978)
[HM2] Hubbard, J., Masur, H.: Quadratic differentials and measured foliations. Acta Math.142, 221–274 (1979)
[Ma] Margulis, G.A.: Arithmeticity of the irreducible lattices in the semi-simple groups of rank greater than 1. Invent. Math.76, 93–120 (1984)
[M] Miller, E.: The homology of the moduli space and the mapping class group. (Preprint 1982)
[Mi] Minkowski, H.: Zur Theorie der positiven quadratischen Formen. J. Crelle101, 196–202 (1887)
[Mo] Morita, S.: Characteristic classes of surface bundles I. (Preprint 1984)
[Mu] Mumford, D.: Abelian quotients of the Teichmüller modular group. J. Anal. Math.18, 227–244 (1967)
[P] Powell, J.: Two theorems on the mapping class group of a surface. Proc. Am. Math. Soc.68, 347–350 (1978)
[S] Strebel, K.: On quadratic differnetials with closed trajectories and second order poles. J. Anal. Math.19, 373–382 (1967)
[S1] Strebel, K.: Quadratic Differentials. Erg. der Math. und ihrer Grenz. 5. Berlin-Heidelberg. New York-Tokyo: Springer 1984
[S2] Serre, J. P.: Cohomology des groupes discrets. In: Prospect in Mathematics. Ann. Math. Stud.70, 77–169 (1971)
[So] Soulé, C.: The cohomology ofSL 3 (Z). Topology17, 1–22 (1978)
[Wa] Wall, C.T.C.: Finiteness conditions forCW-complexes. Ann. Math.81, 56–69 (1965)
[W] Wolpert, S.: On the homology of the moduli space of curves. Ann. Math.118, 491–523 (1983)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Harer, J.L. The virtual cohomological dimension of the mapping class group of an orientable surface. Invent Math 84, 157–176 (1986). https://doi.org/10.1007/BF01388737
Issue Date:
DOI: https://doi.org/10.1007/BF01388737