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Dehn surgery on the figure 8 knot: Immersed surfaces
Author(s):
I.
R.
Aitchison;
S.
Matsumoto;
J.
H.
Rubinstein
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2437-2442.
MSC (1991):
Primary 57Q35;
Secondary 57M50
Posted:
March 24, 1999
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Abstract:
It is known that about 70% of surgeries on the figure 8 knot give manifolds which contain immersed incompressible surfaces. We improve this to about 80% by giving a very simple proof that all even surgeries give manifolds containing such a surface. Moreover, we give a quick proof that every  surgery is virtually Haken, thereby partially dealing with some exceptional cases in Baker's results.
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Additional Information:
I.
R.
Aitchison
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia
Email:
iain@maths.mu.oz.au
S.
Matsumoto
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia
Email:
saburo@is.titech.ac.jp
J.
H.
Rubinstein
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia
Email:
rubin@maths.mu.oz.au
DOI:
10.1090/S0002-9939-99-04716-4
PII:
S 0002-9939(99)04716-4
Keywords:
Cubed manifolds,
immersed incompressible surfaces,
dihedral cover,
Dehn surgery
Received by editor(s):
November 12, 1996
Received by editor(s) in revised form:
October 21, 1997
Posted:
March 24, 1999
Additional Notes:
This research was partially supported by the Australian Research Council.
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
1999,
American Mathematical Society
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