Embedding strings in the unknot.
| dc.contributor.author | Montesinos Amilibia, José María | |
| dc.date.accessioned | 2023-06-20T18:48:11Z | |
| dc.date.available | 2023-06-20T18:48:11Z | |
| dc.date.issued | 2003 | |
| dc.description | Dedicated with respect and friendship to Professor Yukio Matsumoto on his 60th birthday | |
| dc.description.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. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/22294 | |
| dc.identifier.issn | 1340-5705 | |
| dc.identifier.officialurl | http://journal.ms.u-tokyo.ac.jp/ | |
| dc.identifier.relatedurl | http://journal.ms.u-tokyo.ac.jp/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58661 | |
| dc.issue.number | 4 | |
| dc.journal.title | Journal of Mathematical Sciences. The University of Tokyo | |
| dc.language.iso | eng | |
| dc.page.final | 660 | |
| dc.page.initial | 631 | |
| dc.publisher | Graduate School of Mathematical Sciences | |
| dc.relation.projectID | BMF-2002-04137-C02-01. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 515.1 | |
| dc.subject.keyword | strings | |
| dc.subject.keyword | knots. | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Embedding strings in the unknot. | |
| dc.type | journal article | |
| dc.volume.number | 10 | |
| dcterms.references | Bing, R. H., Snake-like continua, Duke Math. J. 18 (1951), 653–663. Bing, R. H., A simple closed curve is the only homogeneous bounded plane continuum that contains an arc, Canad. J. Math. 12 (1960), 209–230. Brown, Morton, The monotone union of open n-cells is an open n-cell, Proc. Amer. Math. Soc. 12 (1961), 812–814. Brown, Morton, A proof of the generalized Schoenflies theorem, Bull. Amer. Math. Soc. 66 (1960), 74–76. Daverman, R. J., Decompositions of manifolds, Pure and Applied Mathematics, 124, Academic Press, Inc., Orlando, FL, 1986. Fox, Ralph H., A remarkable simple closed curve, Ann. of Math. (2) 50 (1949), 264–265. Haken, W., Some results on surfaces in 3-manifolds, 1968 Studies in Modern Topology pp. 39–98 Math. Assoc. Amer. (distributed by Prentice-Hall, Englewood Cliffs, N.J.) Kister, J. M. and D. R. McMillan, Jr., Locally euclidean factors of E4 which cannot be imbedded in E3, Ann. of Math. (2) 76 (1962), 541–546. McMillan, D. R., Jr., Some contractible open 3-manifolds, Trans. Amer. Math. Soc. 102 (1962) 373–382. Montesinos-Amilibia, J. M., Open 3-manifolds, wild subsets of S3 and branched coverings, Revista Matemática Complutense (to appear). cf. Morse, Marston, A reduction of the Schoenflies extension problem, Bull. Amer. Math. Soc. 66 (1960) 113–115. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 7097502e-a5b0-4b03-b547-bc67cda16ae2 | |
| relation.isAuthorOfPublication.latestForDiscovery | 7097502e-a5b0-4b03-b547-bc67cda16ae2 |
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