Boundary structure of hyperbolic $3$-manifolds admitting annular fillings at large distance
HTML articles powered by AMS MathViewer
- by Sangyop Lee PDF
- Proc. Amer. Math. Soc. 134 (2006), 2767-2770 Request permission
Abstract:
We show that if a hyperbolic $3$-manifold $M$ with $\partial M$ a union of tori admits two annular Dehn fillings at distance $\Delta \ge 3$, then $M$ is bounded by at most three tori.References
- 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
- C. McA. Gordon, Boundary slopes of punctured tori in $3$-manifolds, Trans. Amer. Math. Soc. 350 (1998), no. 5, 1713–1790. MR 1390037, DOI 10.1090/S0002-9947-98-01763-2
- Cameron McA. Gordon, Small surfaces and Dehn filling, Proceedings of the Kirbyfest (Berkeley, CA, 1998) Geom. Topol. Monogr., vol. 2, Geom. Topol. Publ., Coventry, 1999, pp. 177–199. MR 1734408, DOI 10.2140/gtm.1999.2.177
- Cameron McA. Gordon and Ying-Qing Wu, Toroidal and annular Dehn fillings, Proc. London Math. Soc. (3) 78 (1999), no. 3, 662–700. MR 1674841, DOI 10.1112/S0024611599001823
- Cameron McA. Gordon and Ying-Qing Wu, Annular Dehn fillings, Comment. Math. Helv. 75 (2000), no. 3, 430–456. MR 1793797, DOI 10.1007/s000140050135
- Chaim Goodman-Strauss, On composite twisted unknots, Trans. Amer. Math. Soc. 349 (1997), no. 11, 4429–4463. MR 1355072, DOI 10.1090/S0002-9947-97-01627-9
- S. Lee, and M. Teragaito, Boundary structure of hyperbolic $3$-manifolds admitting annular and toroidal fillings at large distance, to appear in Canad. J. Math.
- Ruifeng Qiu, Reducible Dehn surgery and annular Dehn surgery, Pacific J. Math. 192 (2000), no. 2, 357–368. MR 1744575, DOI 10.2140/pjm.2000.192.357
- 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, Sutured manifold hierarchies, essential laminations, and Dehn surgery, J. Differential Geom. 48 (1998), no. 3, 407–437. MR 1638025
Additional Information
- Sangyop Lee
- Affiliation: School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Dongdaemun-gu, Seoul 130-722, Korea
- Email: slee@kias.re.kr
- Received by editor(s): January 27, 2005
- Received by editor(s) in revised form: March 21, 2005
- Published electronically: March 21, 2006
- Communicated by: Ronald A. Fintushel
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 2767-2770
- MSC (2000): Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-06-08257-8
- MathSciNet review: 2213757