Décomposition des polyèdres : le point sur le troisième problème de Hilbert

 Access to full text

 Full (PDF)

1. [1] V.G. Boltianskii - Hilbert's third problem, traduit par R.A. Silverman, Winston and Sons, Washington, 1978. Zbl0388.51001MR500434
2. [2] F.E. Browder (Editeur) - Mathematical developments arising from Hilbert problems, Proc. Symp. Pure Math. vol XXVIII (en deux parties) , American Mathematical Society, Providence, 1976. Zbl0326.00002MR419125
3. [3] Euclide - The thirteen books of Euclid's Elements, présentés par T.L. Heath, en 3 volumes, Dover, New York, 1976. Zbl0071.24203
4. [4] P.J. Federico - Descartes on polyhedra (a study of the "De Solidorum Elementis"), Springer, Berlin, 1982. Zbl0498.01004MR680214
5. [5] H. Hadwiger - Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer, Berlin, 1957. Zbl0078.35703MR102775
6. [6] D. Hilbert - Gesammelte Abhandlungen, 3 vol., Chelsea, New York, 1965. 
7. [7] D. Hilbert - Grundlagen der Geometrie, 11e édition, Teubner, Stuttgart, 1968. MR229120
8. [8] I. Lakatos - Proofs and refutations (The logic of mathematical discovery) , Cambridge University Press, Cambridge, 1976. Zbl0334.00022MR479916
9. [9] C.H. Sah - Hilbert's third problem : scissors congruence, Pitman, London, 1979. Zbl0406.52004
10. [10] R. Bricard - Sur une question de géométrie relative aux polyèdres, Nouv. Ann. Math.15(1896), p. 331-334. JFM27.0407.02
11. [11] M. Dehn - Über raumgleiche Polyeder, Nachr. Akad. Wiss., Göttingen, Math.-Phys. K1.1900, p. 345-354. Zbl31.0505.02JFM31.0505.02
12. [12] M. Dehn - Über den Rauminhalt, Math. Ann.55(1902), p. 465-478. Zbl32.0486.01MR1511157JFM32.0486.01
13. [13] H. Hadwiger - Translative Zerlegungsgleichheit der Polyeder des gewöhnlichen Raumes, J. Reine Angew. Math.233(1968), p. 200-212. Zbl0167.19001MR238178
14. [14] H. Hadwiger und P. Glur - Zerlegungsgleichheit ebener Polygone, Elem. Math.6 (1951), p. 97-106. MR45400
15. [15] B. Jessen - The algebra of polyhedra and the Dehn - Sydler theorem, Math. Scand.22(1968), p. 241-256. Zbl0183.49803MR251633
16. [16] B. Jessen, J. Karpf and A. Thorup - Some functional equations in groups and rings, Math. Scand.22(1968), p. 257-265. Zbl0183.04004MR284739
17. [17] B. Jessen and A. Thorup - The algebra of polytopes in affine spaces, Math. Scand.43(1978), p. 211-240. Zbl0398.51009MR531303
18. [18] J.-P. Sydler - Sur la décomposition des polyèdres, Comment. Math. Helv.16 (1943/4), p. 266-273. Zbl0060.34312MR11552
19. [19] J.-P. Sydler - Conditions nécessaires et suffisantes pour l'équivalence des polyèdres de l'espace euclidien à trois dimensions, Comment. Math. Helv.40(1965), p. 43-80. Zbl0135.20906MR192407
20. [20] V.B. Zylev - Equicomposability of equicomplementable polyhedra, Sov. Math. Doklady161(1965), p. 453-455. Zbl0132.14604
21. [21] V.B. Zylev - G-composedness and G-complementability, Sov. Math. Doklady179 (1968), p. 403-404. Zbl0181.26302MR226480
22. [22] J.-L. Cathelineau - Remarques sur l'homologie de SO(n,R) considéré comme groupe discret, C.R. Acad. Sci. Paris, Série I, 295 (1982) , p. 281-283. Zbl0515.20029MR681598
23. [23] J.L. Dupont - Algebra of polytopes and homology of flag complexes, Osaka J. Math.19(1982), p. 599-641. Zbl0499.51014MR676240
24. [24] J.L. Dupont and C.H. Sah - Scissor congruences II, Journ. Pure Appl. Algebra, 25(1982), p. 159-195. Zbl0496.52004MR662760
25. [25] G. Lusztig - The discrete series of GLn over a finite field, Annals of Math. Studies81, Princeton University Press, Princeton, 1974. Zbl0293.20038MR382419
26. [26] C.H. Sah - Scissor Congruences, I : The Gauss - Bonnet map, Math. Scand.49 (1981), p. 181-210. Zbl0496.52003MR661890
27. [27] R.C. Alperin and R.K. Dennis - K2 of quaternion algebras, J. Algebra56 (1979) , p. 262-273. Zbl0397.18011MR527169
28. [28 ] S. Bloch -Higher regulators, algebraic K-theory and regulators of elliptic curves, Publ. Math. IHES, 
29. [29 ] J. Cheeger - Invariants of flat bundles, in Proc. Int. Congr. Math., Vancouver, 1974, p. 3-6. Zbl0332.55020MR423364
30. [30] J. Cheeger and J. Simdns - Differential characters and geometric invariants, Prépublication datée 1973. 
31. [31 ] S. Chern and J. Simons - Characteristic forms and geometric invariants, Ann. of Math.99(1974), p. 48-69. Zbl0283.53036MR353327
32. [32] J.L. Dupont, W. Parry and C.H. Sah - Schur multipliers of classical Lie groups II, à paraître. 
33. [33 ] E.M. Friedlander and G. Mislin - Cohomology of classifying spaces of complex Lie groups and related discrete groups, Comment. Math. Helv.59(1984), p. 347-361. Zbl0548.55016MR761803
34. [34] M. Karoubi - Homology of the infinite orthogonal and symplectic groups over algebraically closed fields, Inv. Math.73(1983), p. 247-250. Zbl0514.18009MR714091
35. [35] J. Milnor - On the homology of Lie groups made discrete, Comment. Math. Helv.58(1983), p. 72-85. Zbl0528.20033MR699007
36. [36] W. Parry and C.H. Sah - Third homology of SL(2,R) made discrete, Journ. Pure Appl. Algebra30(1983), p. 181-209. Zbl0527.18006MR722372
37. [37] D. Quillen - On the cohomology and K-theory of the general linear group over a finite field, Ann. of Math.96(1972), p. 552-586. Zbl0249.18022MR315016
38. [38] C.H. Sah - Schur multipliers of classical Lie groups, I, à paraître. 
39. [39] C.H. Sah and J.B. Wagoner - Second homology of Lie groups made discrete, Comm. in Algebra, 5(1977), p. 611-642. Zbl0375.18006MR646087
40. [40] A. Suslin - Stability in algebraic K-theory, Springer Lecture Notes in Math. vol. 967 (1982), p. 304-333. Zbl0498.18008MR689381
41. [41] A. Suslin - Homology of GLn , characteristic classes and Milnor K-theory, Lecture Notes Math., vol. 1046 (1984), p. 357-375. Zbl0528.18007MR750690
42. [42] A. Suslin - On the K-theory of algebraically closed fields, Inv. Math.73 (1983), p. 241-245. Zbl0514.18008MR714090
43. [43] A. Suslin - On the K-theory of local fields, Journ. Pure App. Algebra34 (1984), p. 301-318. Zbl0548.12009MR772065
44. [44] P. Blanc - (Co)homologie différentiable et changement de groupe, Astérisque vol. 124-125, 1985, p. 13-29. Zbl0563.57023
45. [45] A. Haefliger - Sur les classes caractéristiques des feuilletages, Sém. Bourbaki, n° 412 (Juin 1972), Lecture Notes in Mathematics, vol. 317, 1973. Zbl0257.57011MR420655
46. [46] A. Haefliger - The homology of nilpotent Lie groups made discrete, Astérisque vol. 113-114, 1984, p. 206-211. Zbl0546.55021MR749059
47. [47] W.T. Van Est - A generalization of the Cartan - Leray spectral sequence, Nederl. Akad. Weten. Proc. Serie A, 61(1958), p. 399-405 et 406-413. Zbl0084.39202
48. [48] K. Aomoto - Analytic structure of Schläfli function, Nagoya Math. Journ.68 (1977), p. 1-16. Zbl0382.33010MR569685
49. [49] H.S.M. Coxeter - The functions of Schläfli and Labatschefsky, Quart. J. Math. (Oxford)6(1935), p. 13-29. JFM61.0395.02
50. [50] L. Lewin - Polylogarithms and associated functions, North Holland, New York, 1981. Zbl0465.33001MR618278
51. [51] J. Milnor - Hyperbolic geometry : the first 150 years, Bull. Amer. Math. Soc.6(1982), p. 9-24. Zbl0486.01006MR634431
52. [52] J. Milnor - On the Schläfli differential equality, à paraître. 
53. [53] Schläfli - On the multiple integral ∫n dx dy ... dz where limits are p1 = a1x+b1y+ ... +h1z>0,p2>0,...,pn>0 , and x2+y2+...+z2<1 , in Gesammelte Mathematische Abhandlungen II, Birkhaüser Verlag, Basel, 1953, p. 219-270. 
54. [54] Lobatchevski - La théorie des parallèles (réimpression 1980 de la traduction Houel), Monom Editeur. Zbl0497.51001MR636509
55. [55] C. Roger - Caractères différentiels, in Differential Geometry and Topology (Journées de Dijon 1974), Lect. Notes in Math., vol. 484, Springer, 1975. Zbl0332.57008MR397748

1. Michel Brion, Points entiers dans les polytopes convexes
2. Jean-Louis Cathelineau, The tangent complex to the Bloch-Suslin complex
3. Jean-Michel Kantor, Les problèmes de Hilbert et leur devenir
4. Pierre Cartier, Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents
5. Jean-Louis Cathelineau, Homologie du groupe linéaire et polylogarithmes
6. Jean-Marc Schlenker, La conjecture des soufflets