Dehn filling, reducible 3-manifolds, and Klein bottles
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- by Seungsang Oh PDF
- Proc. Amer. Math. Soc. 126 (1998), 289-296 Request permission
Abstract:
Let $M$ be a compact, connected, orientable, irreducible 3-manifold whose boundary is a torus. We announce that if two Dehn fillings create reducible manifold and manifold containing Klein bottle, then the maximal distance is three.References
-
S. Boyer and X. Zhang, Finite Dehn Surgery on Knots, J. Amer. Math. Soc. 9 (1996), 1005–1050. CMP 96:15.
- S. Boyer and X. Zhang, The Semi-norm and Dehn Filling, preprint.
- S. Boyer and X. Zhang, Reducing Dehn Filling and Toroidal Dehn Filling, preprint.
- Marc Culler, C. McA. Gordon, J. Luecke, and Peter B. Shalen, Dehn surgery on knots, Ann. of Math. (2) 125 (1987), no. 2, 237–300. MR 881270, DOI 10.2307/1971311
- Cameron McA. Gordon, Dehn surgery on knots, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990) Math. Soc. Japan, Tokyo, 1991, pp. 631–642. MR 1159250
- C. Gordon, Boundary slopes of punctured tori in 3-manifolds, preprint.
- C. McA. Gordon and J. Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989), no. 2, 371–415. MR 965210, DOI 10.1090/S0894-0347-1989-0965210-7
- C. Gordon and J. Luecke, Reducible manifolds and Dehn surgery, Topology 35 (1996), 385–409.
- C. McA. Gordon and J. Luecke, Dehn surgeries on knots creating essential tori. I, Comm. Anal. Geom. 3 (1995), no. 3-4, 597–644. MR 1371211, DOI 10.4310/CAG.1995.v3.n4.a3
- C. McA. Gordon and R. A. Litherland, Incompressible planar surfaces in $3$-manifolds, Topology Appl. 18 (1984), no. 2-3, 121–144. MR 769286, DOI 10.1016/0166-8641(84)90005-1
- William Jaco, Lectures on three-manifold topology, CBMS Regional Conference Series in Mathematics, vol. 43, American Mathematical Society, Providence, R.I., 1980. MR 565450, DOI 10.1090/cbms/043
- S. Oh, Reducible and toroidal 3-manifolds obtained by Dehn fillings, Topology and its Appl. 75 (1997), 93–104.
- H. Rubinstein, On 3-manifolds that have finite fundamental groups and contain Klein bottles, Trans. Amer. Math. Soc. 251 (1979) 129-137.
- 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
- Ying Qing Wu, The reducibility of surgered $3$-manifolds, Topology Appl. 43 (1992), no. 3, 213–218. MR 1158868, DOI 10.1016/0166-8641(92)90157-U
- Y. Wu, Dehn fillings producing reducible manifold and toroidal manifold, preprint.
Additional Information
- Seungsang Oh
- Email: soh@math.utexas.edu
- Received by editor(s): April 8, 1996
- Received by editor(s) in revised form: May 31, 1996
- Communicated by: Ronald Fintushel
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 289-296
- MSC (1991): Primary 57M25, 57M99, 57N10
- DOI: https://doi.org/10.1090/S0002-9939-98-03978-1
- MathSciNet review: 1402882