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

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References

  1. Cartier, P., Décomposition des polyèdres: Le point sur le Troisième Problème de Hilbert.Seminaire N. Bourbaki, no. 646 (1984–85).

  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.

    MATH  MathSciNet  Google Scholar 

  3. —, Sur l'homologie deSL 2 a coefficients dans l'action adjointe.Math. Scand., 63 (1988), 51–86.

    MATH  MathSciNet  Google Scholar 

  4. Connes, A., Non commutative differential geometry.Inst. Hautes Études Sci. Publ. Math., 62 (1985), 41–144, 257–360.

    MATH  Google Scholar 

  5. Dupont, J. L., Algebra of polytopes and homology of flag complexes.Osaka J. Math., 19 (1982), 599–641.

    MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  7. Dupont, J. L. &Sah, C. H., Scissors congruences, II.J. Pure Appl. Algebra, 25 (1982), 159–195.

    Article  MATH  MathSciNet  Google Scholar 

  8. Hochschild, G., Kostant, B. &Rosenberg, A., Differential forms on regular affine algebras.Trans. Amer. Math. Soc., 102 (1962), 383–408.

    Article  MATH  MathSciNet  Google Scholar 

  9. Jessen, B., The algebra of polyhedra and the Dehn-Sydler theorem.Math. Scand., 22 (1968), 241–256.

    MATH  MathSciNet  Google Scholar 

  10. —, Zur Algebra der Polytope.Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II (1972), 47–53.

    MATH  MathSciNet  Google Scholar 

  11. Jessen, B. &Thorup, A., The algebra of polytopes in affine spaces.Math. Scand., 43 (1978), 211–240.

    MATH  MathSciNet  Google Scholar 

  12. Karoubi, M.,K-théorie multiplicative et homologie cyclique.C. R. Acad. Sci. Paris Sér. I, 303 (1986), 507–510.

    MATH  MathSciNet  Google Scholar 

  13. Loday, J.-L. &Quillen, D., Cyclic homology and the Lie algebra homology of matrices.Commment. Math. Helv., 59 (1984), 565–591.

    MATH  MathSciNet  Google Scholar 

  14. MacLane, S.,Homology. Grundl. Math. Wiss. 114, SpringerVerlag, Berlin-Göttingen-Heidelberg, 1963.

    MATH  Google Scholar 

  15. May, J. P.,Simplical Objects in Algebraic Topology. D. Van Nostrand Co., Toronto-London-Melbourne, 1967.

    Google Scholar 

  16. Sah, C. H.,Hilbert's Third Problem: Scissors Congruences. Res. Notes in Math. 33, Pitman, London, 1979.

    Google Scholar 

  17. —, Homology of classical Lie groups made discrete, I. Stability theorems and Schur multipliers,Comment. Math. Helv., 61 (1986), 308–347.

    MATH  MathSciNet  Google Scholar 

  18. —, Homology of classical Lie groups made discrete, III.J. Pure Appl. Algebra, 56 (1989), 269–312.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    MATH  MathSciNet  Google Scholar 

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This work is partially supported by grants from Statens Naturvidenskabelige Forskningsråd, Denmark, the National Science Foundation, U.S.A., and the Paul and Gabriella Rosenbaum Foundation, U.S.A.

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Dupont, J.L., Sah, CH. Homology of Euclidean groups of motions made discrete and Euclidean scissors congruences. Acta Math 164, 1–27 (1990). https://doi.org/10.1007/BF02392750

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