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Embedding strings in the unknot.

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Montesinos Amilibia, José María (2003) Embedding strings in the unknot. Journal of Mathematical Sciences. The University of Tokyo, 10 (4). pp. 631-660. ISSN 1340-5705

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Official URL: http://journal.ms.u-tokyo.ac.jp/


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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.


Item Type:Article
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Dedicated with respect and friendship to Professor Yukio Matsumoto on his 60th birthday

Uncontrolled Keywords:strings; knots.
Subjects:Sciences > Mathematics > Topology
ID Code:22294
Deposited On:09 Jul 2013 17:12
Last Modified:12 Dec 2018 15:13

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