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.

References in corpus (3)

• A finite-dimensional TQFT for three-manifolds based on group PSL(2, C) and cross-ratios
• Invariants of three-dimensional manifolds from four-dimensional Euclidean geometry
• A simple topological quantum field theory for manifolds with triangulated boundary

Cited by in corpus (4)

• Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves
• A finite-dimensional TQFT for three-manifolds based on group PSL(2, C) and cross-ratios
• A simple topological quantum field theory for manifolds with triangulated boundary
• Invariants of three-dimensional manifolds from four-dimensional Euclidean geometry