GEOMETRIC QUOTIENTS OF LINK GROUPS

A geometric method is given for finding quotients of a link group using the geometry of a projection of the link. The method is called ''contraction of bands''. If a projection of the link is chosen, a spanning surface of the link is constructed which decomposes as discs connected by maximal bands. These are the bands involved in the contraction method. When all the bands are contracted, a quotient is obtained all of whose relations are of Artin-type; this is called the ''Artin quotient''. It is possible that the Artin quotient is a quotient of a classical Artin group. However, it is shown in this paper that any Artin group is the quotient of some link group. Involved in this is an interesting class of links called ''minimal Artin links''. The paper contains examples of various contractions and Artin quotients.