AN ANALOGUE OF TURAEV COMULTIPLICATION FOR KNOTSIN NON-ORIENTABLE THICKENING OF A NON-ORIENTABLE SURFACE (2025)
Выпуск:
Т. 10 № 1 (2025)
This paper concerns pseudo-classical knots in the non-orientable manifold Σˆ = Σ × [0, 1], where Σ is a non-orientable surface and a knot K ⊂ Σˆ is called pseudo-classical if Kis orientation-preserving path in Σˆ. For this kind of knot we introduce an invariant ∆that is an analogue of Turaev comultiplication for knots in a thickened orientable surface. As its classical prototype, ∆ 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 ∆, including an analogue of the affine index polynomial.