New Whitney-type formulas for plane curves. (English) Zbl 0928.57004
Tabachnikov, S. (ed.), Differential and symplectic topology of knots and curves. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 190(42), 103-111 (1999).
The classical Whitney formula relates the algebraic number of times that a generic immersed plane curve intersects the Whitney index, or winding number, of this curve. The author gives a nice generalization of the formula, showing that this is just the simplest one in an infinite family of identities. These identities express the Whitney index of a plane curve in terms of some functions defined at double points of the curve.
For the entire collection see [Zbl 0910.00021].
For the entire collection see [Zbl 0910.00021].
Reviewer: Andrei Vesnin (Novosibirsk)
MSC:
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
| 57R42 | Immersions in differential topology |
