To any compactly supported, area preserving, piecewise linear homeomorphism of the plane is associated a relation in 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 of certain function fields are found.
À tout homéomorphisme linéaire par morceaux à support compact du plan qui préserve l’aire est associée une relation dans le 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 de certains corps de fonctions.
@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}, pages = {133--148}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {48}, number = {1}, year = {1998}, doi = {10.5802/aif.1613}, zbl = {0904.19001}, mrnumber = {99d:19001}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1613/} }
TY - JOUR AU - Greenberg, Peter TI - Area preserving pl homeomorphisms and relations in $K_2$ JO - Annales de l'Institut Fourier PY - 1998 SP - 133 EP - 148 VL - 48 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1613/ DO - 10.5802/aif.1613 LA - en ID - AIF_1998__48_1_133_0 ER -
%0 Journal Article %A Greenberg, Peter %T Area preserving pl homeomorphisms and relations in $K_2$ %J Annales de l'Institut Fourier %D 1998 %P 133-148 %V 48 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1613/ %R 10.5802/aif.1613 %G en %F AIF_1998__48_1_133_0
Greenberg, Peter. Area preserving pl homeomorphisms and relations in $K_2$. Annales de l'Institut Fourier, Volume 48 (1998) no. 1, pp. 133-148. doi : 10.5802/aif.1613. https://aif.centre-mersenne.org/articles/10.5802/aif.1613/
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