Integrating a weight system of order \(n\) to an invariant of \((n-1)\)-singular knots. (English) Zbl 0868.57010
Summary: Starting from a weight-system denoted by \(P\) and defined on the \(n\)-chord-diagrams with values in an arbitrary \(\mathbb{Q}\)-module, we give an explicit combinatorial formula for an invariant of \((n-1)\)-singular knots which has \(P\) as its derivative. The formula is defined for regular knot projections. Its invariance under singular Reidemeister moves is then proved.
MSC:
57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
57R45 | Singularities of differentiable mappings in differential topology |