AREA-PRESERVING PL HOMEOMORPHISMS AND RELATIONS IN K-2

To any compactly supported, area preserving, piecewise linear homeomor phism of the plane is associated a relation in K-2 of the smallest fie ld whose elements are needed to write the homeomorphism. Using a formu la of J. Morita, we show how to calculate the relation, in some simple cases. As applications, a ''reciprocity'' formula for a pair of trian gles in the plane, and some explicit elements of torsion in K-2 of cer tain function fields are found.