A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds
Geometric Topology
2014-11-12 v5 Mathematical Physics
Algebraic Topology
math.MP
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
Cite
@article{arxiv.math/0605164,
title = {A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds},
author = {Jérôme Dubois and Igor G. Korepanov and Evgeniy V. Martyushev},
journal= {arXiv preprint arXiv:math/0605164},
year = {2014}
}