Vol. 27, No. 2, 1968

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Proving that wild cells exist

P. H. Doyle, III and John Gilbert Hocking

Vol. 27 (1968), No. 2, 265–266

In their famous paper Fox and Artin constructed several examples of wild cells in 3-space. The present authors construct a wild disk D in the 4-sphere S4 with the property that the proof of nontameness is perhaps the most elementary possible. We require only the knowledge that if K is the trefoil knot in the 3-sphere S3, then the fundamental group π1(S3 K) is not abelian. Parenthetically, the wild disk D constructed here has the property that every arc on D is tame, a fact which follows immediately from the construction.

Mathematical Subject Classification
Primary: 54.78
Received: 4 January 1968
Published: 1 November 1968
P. H. Doyle, III
John Gilbert Hocking