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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2010
• ISSN: 1815-0659
• 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
• 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.

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...