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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/
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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Additional Information: | 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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