Area preserving pl homeomorphisms and relations in K 2

Peter Greenberg

Annales de l'institut Fourier (1998)

  • Volume: 48, Issue: 1, page 133-148
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Greenberg, Peter. "Area preserving pl homeomorphisms and relations in $K_2$." Annales de l'institut Fourier 48.1 (1998): 133-148. <http://eudml.org/doc/75273>.

@article{Greenberg1998,
abstract = {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.},
author = {Greenberg, Peter},
journal = {Annales de l'institut Fourier},
keywords = {algebraic -theory; ; piecewise linear homeomorphisms; torsion},
language = {eng},
number = {1},
pages = {133-148},
publisher = {Association des Annales de l'Institut Fourier},
title = {Area preserving pl homeomorphisms and relations in $K_2$},
url = {http://eudml.org/doc/75273},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Greenberg, Peter
TI - Area preserving pl homeomorphisms and relations in $K_2$
JO - Annales de l'institut Fourier
PY - 1998
PB - Association des Annales de l'Institut Fourier
VL - 48
IS - 1
SP - 133
EP - 148
AB - 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.
LA - eng
KW - algebraic -theory; ; piecewise linear homeomorphisms; torsion
UR - http://eudml.org/doc/75273
ER -

References

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  6. [GS] P. GREENBERG, V. SERGIESCU, C1 piecewise projective homeomorphisms and a noncommutative Steinberg extension, J. K-Theory, 9 (1995), 529-544. Zbl0969.57027MR97c:57037
  7. [Li] S. LICTENBAUM, Groups related to scissors congruence groups, Contemp. Math., 83 (1989), 151-157. Zbl0674.55012MR90e:20030
  8. [Mil] J. MILNOR, Introduction to Algebraic K-Theory Annals of Math. Studies 72, Princeton Univ. Press, N.J., 1971. Zbl0237.18005
  9. [Mor] J. MORITA, K2SL2 of Euclidean domains, generalized Dennis-Stein symbols and a certain three-unit formula, J. Pure and Applied Alg., 79 (1992), 51-61. Zbl0759.19003
  10. [PS] W. PARRY and C.H. SAH, Third homology of SL2R made discrete, J. Pure and Applied Alg., 30 (1983), 181-209. Zbl0527.18006MR85f:20043

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