Geometry of Whitney-type formulas. (English) Zbl 1050.57004
Summary: The article contains a generalization of the classical Whitney formula for the number of double points of a plane curve. This formula is split into a series of equalities, and also extended to curves on a torus, to non-pointed curves, and to wave fronts. All the theorems are given geometric proofs employing logarithmic Gauss-type maps from suitable configuration spaces to \(\mathbb C\).
MSC:
57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
57N35 | Embeddings and immersions in topological manifolds |