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

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.

Keywords

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