KNOT-THEORY AND PLANE ALGEBRAIC-CURVES

Knot theory has been known for a long time to be a powerful tool for t he study of the topology of local isolated singular points of a plane algebraic curve. However it is rather recently that knot theory has be en used to study plane algebraic curves in the large. Given a reduced plane algebraic curve Gamma subset of C-2 passing through the origin, let L-r = Gamma boolean AND partial derivative B-r(4) be the intersect ion of Gamma with a round ball in C-2 of radius r>0 centered at the or igin. When this intersection is transverse, L-r is an oriented link in S-r(3) = partial derivative B-r(4). The main purpose of this paper is to present a survey of the results relating the topology of the pair (S-r(3), L-r) to the topology of the pair (B-r(4) Gamma boolean AND pa rtial derivative B-r(4)). (C) 1998 Elsevier Science Ltd. All rights re served.