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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
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 $(6k,t)$ 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