2024/07/30 by Vladimir Tarkaev, Tarkaev, Vladimir
Computer Science · Engineering · Mathematics · #57M25 #57M27 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Material Science and Thermodynamics
paper · pdf · doi:10.48550/arxiv.2407.20715
openalex publication_date 2024/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper concerns pseudo-classical knots in the non-orientable manifold Σ =Σ× [0,1], where Σ is a non-orientable surface and a knot K ⊂ Σ is called pseudo-classical if K is orientation-preserving path in Σ. For this kind of knot we introduce an invariant Δ that is an analogue of Turaev comultiplication for knots in a thickened orientable surface. As its classical prototype, Δ takes value in a polynomial algebra generated by homotopy classes of non-contractible loops on Σ, however, as a ground ring we use some subring of ℂ instead of ℤ. Then we define a few homotopy, homology and polynomial invariants, which are consequences of Δ, including an analogue of the affine index polynomial.