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
Date:2010
Main Authors: Dubois, J., Korepanov, I.G., Martyushev, E.V.
Format: Article
Language:English
Published: Інститут математики НАН України 2010
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/146349
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-146349
record_format dspace
spelling 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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