Dehn surgery on the figure 8 knot: Immersed surfaces

I. R. AITCHISON, S. MATSUMOTO, AND J. H. RUBINSTEIN(Communicated by Ronald A. Fintushel)Abstract. It is known that about 70% of surgeries on the gure 8 knot givemanifoldswhichcontainimmersedincompressiblesurfaces. Weimprovethis toabout 80% by giving a very simple proof that all even surgeries give manifoldscontaining such a surface. Moreover, we give a quick proof that every (6k;t)surgery is virtually Haken, thereby partially dealing with some exceptionalcases in Baker’s results.

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