$3$-manifold groups with the finitely generated intersection property
HTML articles powered by AMS MathViewer
- by Teruhiko Soma PDF
- Trans. Amer. Math. Soc. 331 (1992), 761-769 Request permission
Abstract:
In this paper, first we consider whether the fundamental groups of certain geometric $3$-manifolds have $\text {FGIP}$ or not. Next we give the sufficient conditions that $\text {FGIP}$ for $3$-manifold groups is preserved under torus sums or annulus sums and connect this result with a conjecture by Hempel $[4]$.References
- Benjamin Baumslag, Intersections of finitely generated subgroups in free products, J. London Math. Soc. 41 (1966), 673–679. MR 199247, DOI 10.1112/jlms/s1-41.1.673
- Leon Greenberg, Discrete groups of motions, Canadian J. Math. 12 (1960), 415–426. MR 115130, DOI 10.4153/CJM-1960-036-8
- John Hempel, $3$-Manifolds, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1976. Ann. of Math. Studies, No. 86. MR 0415619
- John Hempel, The finitely generated intersection property for Kleinian groups, Knot theory and manifolds (Vancouver, B.C., 1983) Lecture Notes in Math., vol. 1144, Springer, Berlin, 1985, pp. 18–24. MR 823280, DOI 10.1007/BFb0075010
- William Jaco, Lectures on three-manifold topology, CBMS Regional Conference Series in Mathematics, vol. 43, American Mathematical Society, Providence, R.I., 1980. MR 565450 O. Kakimizu, Intersections of finitely generated subgroups in a $3$-manifold group, Preprint, Hiroshima Univ., 1988.
- John W. Morgan, On Thurston’s uniformization theorem for three-dimensional manifolds, The Smith conjecture (New York, 1979) Pure Appl. Math., vol. 112, Academic Press, Orlando, FL, 1984, pp. 37–125. MR 758464, DOI 10.1016/S0079-8169(08)61637-2
- G. P. Scott, Finitely generated $3$-manifold groups are finitely presented, J. London Math. Soc. (2) 6 (1973), 437–440. MR 380763, DOI 10.1112/jlms/s2-6.3.437
- G. P. Scott, Compact submanifolds of $3$-manifolds, J. London Math. Soc. (2) 7 (1973), 246–250. MR 326737, DOI 10.1112/jlms/s2-7.2.246
- Peter Scott, The geometries of $3$-manifolds, Bull. London Math. Soc. 15 (1983), no. 5, 401–487. MR 705527, DOI 10.1112/blms/15.5.401
- Jean-Pierre Serre, Trees, Springer-Verlag, Berlin-New York, 1980. Translated from the French by John Stillwell. MR 607504
- William P. Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, 357–381. MR 648524, DOI 10.1090/S0273-0979-1982-15003-0 —, The geometry and topology of $3$-manifolds, Mimeographed Notes, Princeton Univ., Princeton, N.J., 1978.
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 331 (1992), 761-769
- MSC: Primary 57M05; Secondary 30F40, 57N10
- DOI: https://doi.org/10.1090/S0002-9947-1992-1042289-4
- MathSciNet review: 1042289