Dehn surgery on the figure 8 knot:

Immersed surfaces

Authors:
I. R. Aitchison, S. Matsumoto and J. H. Rubinstein

Journal:
Proc. Amer. Math. Soc. **127** (1999), 2437-2442

MSC (1991):
Primary 57Q35; Secondary 57M50

DOI:
https://doi.org/10.1090/S0002-9939-99-04716-4

Published electronically:
March 24, 1999

MathSciNet review:
1485454

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-99-04716-4

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

Published electronically:
March 24, 1999

Additional Notes:
This research was partially supported by the Australian Research Council.

Communicated by:
Ronald A. Fintushel

Article copyright:
© Copyright 1999
American Mathematical Society