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

2006/05/31 by Jérôme Dubois, Igor G. Korepanov, Evgeniy V. Martyushev
Engineering · Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Engineering #Euclidean geometry #Finite type invariant #Geometric and Algebraic Topology #Geometry #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Invariant polynomial #Knot (papermaking) #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Polynomial #Pure mathematics #Topological quantum field theory #Torsion (gastropod) #math-ph #math.AT #math.GT #math.MP #msc:57M27 #msc:57Q10 #msc:57R56

paper · pdf · doi:10.3842/sigma.2010.032

published as SIGMA 6 (2010), 32, 29 pages

openalex publication_date 2010/04/15 · arxiv created 2010/04/22 · arxiv updated 2014/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

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