Uncountably many wild knots whose cyclic branched covering are S3
| dc.contributor.author | Montesinos Amilibia, José María | |
| dc.date.accessioned | 2023-06-20T18:48:09Z | |
| dc.date.available | 2023-06-20T18:48:09Z | |
| dc.date.issued | 2003 | |
| dc.description | Dedicado a Francisco González Acuña en su sexagésimo cumpleaños | |
| dc.description.abstract | According to the confirmed Smith Conjecture [The Smith conjecture (New York, 1979), Academic Press, Orlando, FL, 1984;], a tame knot in the 3-sphere has a cyclic branched covering that is also the 3-sphere only if it is trivial. Here the author produces a nontrivial, wild knot whose n-fold cyclic branched cover is S3, for all n. In fact there are uncountably many inequivalent knots with this property, and the knots can be chosen to bound an embedded disk that is tame in its interior. One might conjecture that any wild knot whose nontrivial n-fold cyclic branched cover is S3 must bound such a disk that is tame in its interior. | |
| 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/22293 | |
| dc.identifier.issn | 1139-1138 | |
| dc.identifier.officialurl | http://www.mat.ucm.es/serv/revmat/vol16-1j.html | |
| dc.identifier.relatedurl | http://www.springer.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58660 | |
| dc.issue.number | 1 | |
| dc.journal.title | Revista matemática complutense | |
| dc.language.iso | eng | |
| dc.page.final | 344 | |
| dc.page.initial | 329 | |
| dc.publisher | Springer | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 515.162 | |
| dc.subject.keyword | decomposition | |
| dc.subject.keyword | wild knot | |
| dc.subject.keyword | branched covering | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Uncountably many wild knots whose cyclic branched covering are S3 | |
| dc.type | journal article | |
| dc.volume.number | 16 | |
| dcterms.references | Armentrout, S. Monotone decompositions of E3, Ann. Math. Stud. 60, 1–25 (1966). Armentrout, Steve; Lininger, Lloyd L.; Meyer, Donald V. Equivalent decompositions of E3, Ann. Math. Stud. 60, 27–31 (1966). Bing, R. H. A homeomorphism between the 3-sphere and the sum of two solid horned spheres. Ann. of Math. (2) 56 (1952) 354–362. Bing, R.H. Inequivalent families of periodic homeomorphisms of E3, Ann. Math. (2) 80, 78–93 (1964). Bing, R.H. The collected papers of R. H. Bing. Vol. 1 and 2. Ed. by Sukhjit Singh, Steve Armentrout and Robert J. Daverman, Providence, RI: American Mathematical Society, xix, 1654 p. (1988). MSC 2000. Blankinship, W.A.; Fox, R.H. Remarks on certain pathological open subsets of 3-space and their fundamental groups. Proc. Am. Math. Soc. 1, 618–624 (1950). Daverman, Robert J. Decompositions of manifolds. Pure and Applied Mathematics, 124. Orlando etc.: Academic Press, Inc., Harcourt Brace Jovanovich, Publishers. XI, 317 p. Fox, Ralph H. Covering spaces with singularities. 1957 A symposium in honor of S. Lefschetz pp. 243–257 Princeton University Press, Princeton, N.J. Freudenthal, H. Über die Enden diskreter Räume und Gruppen. Comment. Math. Helv. 17 (1945)1–38. Lloyd, N. G. Degree theory. Cambridge Tracts in Mathematics, No. 73. Cambridge University Press, Cambridge-New York-Melbourne, 1978. vi+172 pp. ISBN: 0-521-21614-1 Montesinos-Amilibia, J.M. Open 3-manifolds as 3-fold branched coverings. Rev.R. Acad.Cien.SerieA.Mat. 95(2001)1–3. Montgomery, D.; Zippin, L. Examples of transformation groups. Proc. Amer. Math. Soc. 5 (1954) 460–465. Sher, R.B. Concerning wild Cantor sets in E3, Proc. Am. Math. Soc. 19, 1195–1200 (1968). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 7097502e-a5b0-4b03-b547-bc67cda16ae2 | |
| relation.isAuthorOfPublication.latestForDiscovery | 7097502e-a5b0-4b03-b547-bc67cda16ae2 |
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