Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Boundary structure of hyperbolic $ 3$-manifolds admitting annular fillings at large distance

Author(s): Sangyop Lee
Journal: Proc. Amer. Math. Soc. 134 (2006), 2767-2770.
MSC (2000): Primary 57M25
Posted: March 21, 2006
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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:

1.
M. Culler, C. McA. Gordon, J. Luecke, and P.B. Shalen, Dehn surgery on knots, Ann. of Math. 125 (1987), 237-300. MR 0881270 (88a:57026)

2.
C. McA. Gordon, Boundary slopes on punctured tori in $ 3$-manifolds, Trans. Amer. Math. Soc. 350 (1998), 1713-1790. MR 1390037 (98h:57032)

3.
C. McA. Gordon, Small surfaces and Dehn filling, Proceedings of the Kirbyfest (Berkeley, CA, 1999), Geom. Topol. Monogr. 2, 177-199. MR 1734408 (2000j:57036)

4.
C. McA. Gordon and Y.-Q. Wu, Toroidal and annular Dehn fillings, Proc. London Math. Soc. 78 (1999), 662-700. MR 1674841 (2000b:57029)

5.
C. McA. Gordon and Y.-Q. Wu, Annular Dehn fillings, Comment. Math. Helv. 75 (2000), 430-456. MR 1793797 (2001j:57024)

6.
C. Hayashi and K. Motegi, Only single twists on unknots can produce composite knots, Trans. Amer. Math. Soc. 349 (1997), 4465-4479. MR 1355073 (98b:57010b)

7.
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.

8.
R. Qiu, Reducible Dehn surgery and annular Dehn surgery, Pacific J. Math. 192 (2000), 357-368. MR 1744575 (2001b:57036)

9.
W. Thurston, Three dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982) 357-381. MR 0648524 (83h:57019)

10.
Y.-Q. Wu, Sutured manifold hierarchies, essential laminations, and Dehn surgery, J. Diff. Geom. 48 (1998), 407-437. MR 1638025 (99h:57043)


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 57M25

Retrieve articles in all Journals with MSC (2000): 57M25


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

DOI: 10.1090/S0002-9939-06-08257-8
PII: S 0002-9939(06)08257-8
Keywords: Dehn filling, annular manifold
Received by editor(s): January 27, 2005
Received by editor(s) in revised form: March 21, 2005
Posted: March 21, 2006
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google