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Area preserving pl homeomorphisms and relations in K 2

Peter Greenberg — 1998

Annales de l'institut Fourier

To any compactly supported, area preserving, piecewise linear homeomorphism of the plane is associated a relation in K 2 of the smallest field whose elements are needed to write the homeomorphism. Using a formula of J. Morita, we show how to calculate the relation, in some simple cases. As applications, a “reciprocity” formula for a pair of triangles in the plane, and some explicit elements of torsion in K 2 of certain function fields are found.

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