A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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dc.contributor.author	Dubois, J.
dc.contributor.author	Korepanov, I.G.
dc.contributor.author	Martyushev, E.V.
dc.date.accessioned	2019-02-09T09:15:25Z
dc.date.available	2019-02-09T09:15:25Z
dc.date.issued	2010
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 57M27; 57Q10; 57R56
dc.identifier.other	DOI:10.3842/SIGMA.2010.032
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/146349
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA