A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds
We present an invariant of a three-dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. Our invariant is related to a finite...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2010 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146349 |
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| Cite this: | A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds / J. Dubois , Korepanov I.G., Martyushev E.V.// Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. |
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Dubois, J. Korepanov, I.G. Martyushev, E.V. 2019-02-09T09:15:25Z 2019-02-09T09:15:25Z 2010 A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds / J. Dubois , Korepanov I.G., Martyushev E.V.// Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 57M27; 57Q10; 57R56 DOI:10.3842/SIGMA.2010.032 https://nasplib.isofts.kiev.ua/handle/123456789/146349 We present an invariant of a three-dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. Our invariant is related to a finite-dimensional fermionic topological quantum field theory. The authors J.D. and I.G.K. acknowledge support from the Swiss National Science Foundation. In particular, it made possible the visit of I.G.K. to Geneva, where the work on this paper began. The work of I.G.K. and E.V.M. was supported by Russian Foundation for Basic Research, Grants no. 07-01-96005 and 10-01-96010. The work of J.D. was partially supported by the European Community with Marie Curie Intra–European Fellowship (MEIF–CT–2006–025316). While writing the paper, J.D. visited the CRM. He thanks the CRM for hospitality. Finally, we would like to thank the referee for the very attentive reading of the manuscript and constructive criticism. We hope that, following the referee’s comments, we have substantially improved our paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds |
| spellingShingle |
A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds Dubois, J. Korepanov, I.G. Martyushev, E.V. |
| title_short |
A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds |
| title_full |
A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds |
| title_fullStr |
A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds |
| title_full_unstemmed |
A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds |
| title_sort |
euclidean geometric invariant of framed (un)knots in manifolds |
| author |
Dubois, J. Korepanov, I.G. Martyushev, E.V. |
| author_facet |
Dubois, J. Korepanov, I.G. Martyushev, E.V. |
| publishDate |
2010 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We present an invariant of a three-dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. Our invariant is related to a finite-dimensional fermionic topological quantum field theory.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146349 |
| citation_txt |
A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds / J. Dubois , Korepanov I.G., Martyushev E.V.// Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. |
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