Euclidean tetrahedra and knot invariants

2004/05/28 by I. G. Korepanov, Korepanov, I. G.
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT

paper · pdf · doi:10.48550/arxiv.math/0405547

8 pages; a shorter version will be published at http://csc.ac.ru/LANG=en/news/index.html.en

arxiv created 2004/05/28 · openalex publication_date 2004/05/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct knot invariants on the basis of ascribing Euclidean geometric values to a triangulation of sphere S³ where the knot lies. The main new feature of this construction compared to the author's earlier papers on manifold invariants is that now nonzero "deficit angles" (in the terminology of Regge calculus) can also be handled. Moreover, the knot goes exactly along those edges of triangulations that have nonzero deficit angles.

Related

• Invariants of three-dimensional manifolds from four-dimensional Euclidean geometry
• Braid and knot invariants via triangulations and Ptolemy relations I
• Geometric Knot Spaces and Polygonal Isotopy
• Invariants of knotted surfaces from link homology and bridge trisections
• Hyperbolic Knot Theory