Publication: Embedding strings in the unknot.
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2003
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Graduate School of Mathematical Sciences
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Abstract
In this paper, the possibility of embedding a nontrivial string (R3,K) in the trivial knot (S3,U) is investigated. Uncountably many examples are given. The complementary space in S3 of the image of R3 under the embedding is a continuum. Some well-known snake-like continua appear as these residual spaces. The 2-fold coverings of R3 branched over the strings involved are studied. As a consequence, concrete descriptions of the p-adic solenoids are given, and it is shown that the Whitehead continuum is homeomorphic to Bing's snake-like continuum without end points.
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Dedicated with respect and friendship to Professor Yukio Matsumoto on his 60th birthday
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