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

作者：Dubois Jerome^*; Korepanov Igor G; Martyushev Evgeniy V

来源：Symmetry Integrability and Geometry-Methods and Applications, 2010, 6: 032.

DOI：10.3842/SIGMA.2010.032

• Pachner moves
• Reidemeister torsion
• framed knots
• differential relations in Euclidean geometry
• topological quantum field theory

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.

• 出版日期2010