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A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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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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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6, випуск за цей рік
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A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds
Інший ID:
2010 Mathematics Subject Classification: 57M27; 57Q10; 57R56
DOI:10.3842/SIGMA.2010.032
DOI:10.3842/SIGMA.2010.032
Посилання:
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.
Підтримка:
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.
Дата:
2010
Переглядів:
591
Завантажень:
264
Анотація:
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.
