Classification of knotted tori in 2-metastable dimension

Handle URI:
http://hdl.handle.net/10754/562427
Title:
Classification of knotted tori in 2-metastable dimension
Authors:
Cencelj, Matija; Repovš, Dušan; Skopenkov, Mikhail
Abstract:
This paper is devoted to the classical Knotting Problem: for a given manifold N and number m describe the set of isotopy classes of embeddings N → Sm. We study the specific case of knotted tori, that is, the embeddings Sp × Sq → Sm. The classification of knotted tori up to isotopy in the metastable dimension range m > p + 3 2 q + 2, p 6 q, was given by Haefliger, Zeeman and A. Skopenkov. We consider the dimensions below the metastable range and give an explicit criterion for the finiteness of this set of isotopy classes in the 2-metastable dimension: Theorem. Assume that p+ 4 3 q +2 < mp+ 3 2 q +2 and m > 2p+q +2. Then the set of isotopy classes of smooth embeddings Sp × Sq → Sm is infinite if and only if either q + 1 or p + q + 1 is divisible by 4. © 2012 RAS(DoM) and LMS.
KAUST Department:
Visual Computing Center (VCC)
Publisher:
Turpion-Moscow Limited
Journal:
Sbornik: Mathematics
Issue Date:
30-Nov-2012
DOI:
10.1070/SM2012v203n11ABEH004281
ARXIV:
arXiv:0811.2745
Type:
Article
ISSN:
10645616
Sponsors:
The first and second authors were supported in part by the Slovenian Research Agency (grant nos. P1-0292-0101 and J1-4144-0101). The third author was supported in part by the Russian Foundation for Basic Research (grant no. 12-01-00748-a), the Programme of the President of the Russian Federation for the Support of Young Scientists (grant no. MK-3965.2012.1), the "Dynasty" Foundation and the Simons Foundation.
Additional Links:
http://arxiv.org/abs/arXiv:0811.2745v3
Appears in Collections:
Articles; Visual Computing Center (VCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorCencelj, Matijaen
dc.contributor.authorRepovš, Dušanen
dc.contributor.authorSkopenkov, Mikhailen
dc.date.accessioned2015-08-03T10:37:51Zen
dc.date.available2015-08-03T10:37:51Zen
dc.date.issued2012-11-30en
dc.identifier.issn10645616en
dc.identifier.doi10.1070/SM2012v203n11ABEH004281en
dc.identifier.urihttp://hdl.handle.net/10754/562427en
dc.description.abstractThis paper is devoted to the classical Knotting Problem: for a given manifold N and number m describe the set of isotopy classes of embeddings N → Sm. We study the specific case of knotted tori, that is, the embeddings Sp × Sq → Sm. The classification of knotted tori up to isotopy in the metastable dimension range m > p + 3 2 q + 2, p 6 q, was given by Haefliger, Zeeman and A. Skopenkov. We consider the dimensions below the metastable range and give an explicit criterion for the finiteness of this set of isotopy classes in the 2-metastable dimension: Theorem. Assume that p+ 4 3 q +2 < mp+ 3 2 q +2 and m > 2p+q +2. Then the set of isotopy classes of smooth embeddings Sp × Sq → Sm is infinite if and only if either q + 1 or p + q + 1 is divisible by 4. © 2012 RAS(DoM) and LMS.en
dc.description.sponsorshipThe first and second authors were supported in part by the Slovenian Research Agency (grant nos. P1-0292-0101 and J1-4144-0101). The third author was supported in part by the Russian Foundation for Basic Research (grant no. 12-01-00748-a), the Programme of the President of the Russian Federation for the Support of Young Scientists (grant no. MK-3965.2012.1), the "Dynasty" Foundation and the Simons Foundation.en
dc.publisherTurpion-Moscow Limiteden
dc.relation.urlhttp://arxiv.org/abs/arXiv:0811.2745v3en
dc.subjectEmbeddingen
dc.subjectKnotted torusen
dc.subjectLinken
dc.subjectLink mapen
dc.subjectSurgeryen
dc.titleClassification of knotted tori in 2-metastable dimensionen
dc.typeArticleen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalSbornik: Mathematicsen
dc.contributor.institutionInstitute of Mathematics, Physics and Mechanics, Ljubljana, Sloveniaen
dc.contributor.institutionUniversity of Ljubljana, Ljubljana, Sloveniaen
dc.contributor.institutionInstitute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russian Federationen
dc.identifier.arxividarXiv:0811.2745en
kaust.authorSkopenkov, Mikhailen
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