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

[摘要] 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.

[关键词] Pachner moves;Reidemeister torsion;framed knots;dif ferential relations in Euclidean geometry;topological quantum field theory