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

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

2006-05-06

arxiv.org/abs/math/0605164v5

SIGMA 6 (2010), 32, 29 pages

Mathematics

Geometric Topology

Scientific paper

10.3842/SIGMA.2010.032

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.

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