The self-linking number of a closed curve in R-n

We introduce the self-linking number of a smooth closed curve alpha : S-1 - -> R-n with respect to a 3-dimensional vector bundle over the curve, provid ed that some regularity conditions are satisfied. When n = 3, this construc tion gives the classical self-linking number of a closed embedded curve wit h non-vanishing curvature [5]. We also look at some interesting particular cases, which correspond to the osculating or the orthogonal vector bundle o f the curve.