Acta Mathematica

, Volume 164, Issue 1, pp 1–27 | Cite as

Homology of Euclidean groups of motions made discrete and Euclidean scissors congruences

  • Johan L. Dupont
  • Chih-Han Sah
Article

Keywords

Exact Sequence Spectral Sequence Chain Complex Semidirect Product Cyclic Homology 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Cartier, P., Décomposition des polyèdres: Le point sur le Troisième Problème de Hilbert.Seminaire N. Bourbaki, no. 646 (1984–85).Google Scholar
  2. [2]
    Cathelineau, J.-L., Remarques sur l'homologie deSO(n,R) considéré comme groupe discret.C. R. Acad. Sci. Paris Sér. I, 295 (1982), 281–283.MATHMathSciNetGoogle Scholar
  3. [3]
    —, Sur l'homologie deSL 2 a coefficients dans l'action adjointe.Math. Scand., 63 (1988), 51–86.MATHMathSciNetGoogle Scholar
  4. [4]
    Connes, A., Non commutative differential geometry.Inst. Hautes Études Sci. Publ. Math., 62 (1985), 41–144, 257–360.MATHGoogle Scholar
  5. [5]
    Dupont, J. L., Algebra of polytopes and homology of flag complexes.Osaka J. Math., 19 (1982), 599–641.MATHMathSciNetGoogle Scholar
  6. [6]
    Dupont, J. L., Parry, W. &Sah, C. H., Homology of classical Lie groups made discrete, II.H 2,H 3, and relations with scissors congruence.J. Algebra, 113 (1988), 215–260.MATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Dupont, J. L. &Sah, C. H., Scissors congruences, II.J. Pure Appl. Algebra, 25 (1982), 159–195.MATHMathSciNetCrossRefGoogle Scholar
  8. [8]
    Hochschild, G., Kostant, B. &Rosenberg, A., Differential forms on regular affine algebras.Trans. Amer. Math. Soc., 102 (1962), 383–408.MATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    Jessen, B., The algebra of polyhedra and the Dehn-Sydler theorem.Math. Scand., 22 (1968), 241–256.MATHMathSciNetGoogle Scholar
  10. [10]
    —, Zur Algebra der Polytope.Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II (1972), 47–53.MATHMathSciNetGoogle Scholar
  11. [11]
    Jessen, B. &Thorup, A., The algebra of polytopes in affine spaces.Math. Scand., 43 (1978), 211–240.MATHMathSciNetGoogle Scholar
  12. [12]
    Karoubi, M.,K-théorie multiplicative et homologie cyclique.C. R. Acad. Sci. Paris Sér. I, 303 (1986), 507–510.MATHMathSciNetGoogle Scholar
  13. [13]
    Loday, J.-L. &Quillen, D., Cyclic homology and the Lie algebra homology of matrices.Commment. Math. Helv., 59 (1984), 565–591.MATHMathSciNetGoogle Scholar
  14. [14]
    MacLane, S.,Homology. Grundl. Math. Wiss. 114, SpringerVerlag, Berlin-Göttingen-Heidelberg, 1963.MATHGoogle Scholar
  15. [15]
    May, J. P.,Simplical Objects in Algebraic Topology. D. Van Nostrand Co., Toronto-London-Melbourne, 1967.Google Scholar
  16. [16]
    Sah, C. H.,Hilbert's Third Problem: Scissors Congruences. Res. Notes in Math. 33, Pitman, London, 1979.Google Scholar
  17. [17]
    —, Homology of classical Lie groups made discrete, I. Stability theorems and Schur multipliers,Comment. Math. Helv., 61 (1986), 308–347.MATHMathSciNetGoogle Scholar
  18. [18]
    —, Homology of classical Lie groups made discrete, III.J. Pure Appl. Algebra, 56 (1989), 269–312.MATHMathSciNetCrossRefGoogle Scholar
  19. [19]
    Sydler, J. P., Conditions nécessaires et suffisantes pour l'équivalence des polyèdres de l'espace euclidien à trois dimensions.Comment. Math. Helv., 40 (1965), 43–80.MATHMathSciNetGoogle Scholar

Copyright information

© Almqvist & Wiksell 1990

Authors and Affiliations

  • Johan L. Dupont
    • 1
  • Chih-Han Sah
    • 2
  1. 1.Aarhus UniversityAarhus CDenmark
  2. 2.SUNY at Stony BrookNew YorkUSA

Personalised recommendations