Area preserving pl homeomorphisms and relations in K 2
Annales de l'Institut Fourier, Tome 48 (1998) no. 1, p. 133-148
À tout homéomorphisme linéaire par morceaux à support compact du plan qui préserve l’aire est associée une relation dans le K 2 du corps de définition.À l’aide d’une formule de J. Morita, on montre comment calculer la relation dans des cas simples. En appplication, une formule de réciprocité pour des paires de triangles dans le plan est démontrée, et des éléments de torsion sont construits dans le K 2 de certains corps de fonctions.
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.
@article{AIF_1998__48_1_133_0,
     author = {Greenberg, Peter},
     title = {Area preserving pl homeomorphisms and relations in $K\_2$},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {48},
     number = {1},
     year = {1998},
     pages = {133-148},
     doi = {10.5802/aif.1613},
     zbl = {0904.19001},
     mrnumber = {99d:19001},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1998__48_1_133_0}
}
Greenberg, Peter. Area preserving pl homeomorphisms and relations in $K_2$. Annales de l'Institut Fourier, Tome 48 (1998) no. 1, pp. 133-148. doi : 10.5802/aif.1613. https://www.numdam.org/item/AIF_1998__48_1_133_0/

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