Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Virtual cohomological dimension of mapping class groups of 3-manifolds

Author: Darryl McCullough
Journal: Bull. Amer. Math. Soc. 18 (1988), 27-30
MSC (1985): Primary 57M99; Secondary 57S99, 55S37, 20F34
MathSciNet review: 919653
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [B-E] R. Bieri and B. Eckmann, Groups with homological duality generalizing Poincaré duality, Invent. Math. 20 (1973), 103-124. MR 340449
  • Francis Bonahon, Cobordism of automorphisms of surfaces, Ann. Sci. École Norm. Sup. (4) 16 (1983), no. 2, 237–270. MR 732345
  • [G] P. Grasse, Results on finite presentation of mapping class groups of certain 3-manifolds, dissertation, Univ. of Oklahoma, 1986.
  • John L. Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math. 84 (1986), no. 1, 157–176. MR 830043,
  • John L. Harer, The cohomology of the moduli space of curves, Theory of moduli (Montecatini Terme, 1985) Lecture Notes in Math., vol. 1337, Springer, Berlin, 1988, pp. 138–221. MR 963064,
  • W. J. Harvey, Geometric structure of surface mapping class groups, Homological group theory (Proc. Sympos., Durham, 1977) London Math. Soc. Lecture Note Ser., vol. 36, Cambridge Univ. Press, Cambridge-New York, 1979, pp. 255–269. MR 564431
  • W. J. Harvey, Boundary structure of the modular group, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978) Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 245–251. MR 624817
  • Geoffrey Hemion, On the classification of homeomorphisms of 2-manifolds and the classification of 3-manifolds, Acta Math. 142 (1979), no. 1-2, 123–155. MR 512214,
  • William H. Jaco and Peter B. Shalen, Seifert fibered spaces in 3-manifolds, Mem. Amer. Math. Soc. 21 (1979), no. 220, viii+192. MR 539411,
  • Klaus Johannson, Homotopy equivalences of 3-manifolds with boundaries, Lecture Notes in Mathematics, vol. 761, Springer, Berlin, 1979. MR 551744
  • [K] R. Kramer, The twist group of an orientable cube-with-two-handles is not finitely generated, unpublished.
  • [M] J. McCool, Some finitely presented subgroups of the automorphism group of a free group, J. Algebra 35 (1975), 205-213. MR 396764
  • Darryl McCullough, Virtually geometrically finite mapping class groups of 3-manifolds, J. Differential Geom. 33 (1991), no. 1, 1–65. MR 1085134
  • Darryl McCullough and Andy Miller, Homeomorphisms of 3-manifolds with compressible boundary, Mem. Amer. Math. Soc. 61 (1986), no. 344, xii+100. MR 840832,
  • [S] J.-P. Serre, Cohomologie des groupes discrets, Prospects in Mathematics, Ann. of Math. Studies no. 70, Princeton Univ. Press, Princeton, N.J., 1971, pp. 77-169. MR 385006
  • Friedhelm Waldhausen, Recent results on sufficiently large 3-manifolds, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 21–38. MR 520520

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 57M99, 57S99, 55S37, 20F34

Retrieve articles in all journals with MSC (1985): 57M99, 57S99, 55S37, 20F34

Additional Information


American Mathematical Society