Dehn surgery on the figure 8 knot: Immersed surfaces

Authors
Aitchison, IR Matsumoto, S Rubinstein, JH
Citation
Ir. Aitchison et al., Dehn surgery on the figure 8 knot: Immersed surfaces, P AM MATH S, 127(8), 1999, pp. 2437-2442
Citations number
21
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939 → ACNP
Volume
127
Issue
8
Year of publication
1999
Pages
2437 - 2442
Database
ISI
SICI code
0002-9939(199908)127:8<2437:DSOTF8>2.0.ZU;2-Y
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 8 0% by giving a very simple proof that all even surgeries give manifolds con taining 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.