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Classical projective geometry and arithmetic groups

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References

  1. Alexandrov, P.S.: Diskrete Räume. Mat. Sb. (N.S.)2, 501–518 (1937)

    Google Scholar 

  2. Ash, A., Mumford, D., Rapoport, M., Tai, Y.: Smooth compactifications of locally symmetric varieties. In: Lie groups: history, frontiers, and applications, vol. 4, Brookline, Massachusetts, USA, Math. Sci. Press 1975

    Google Scholar 

  3. Ash, A.: Deformation retracts with lowest possible dimension of arithmetic quotients of self-adjoint homogeneous cones. Math. Ann.225, 69–76 (1977)

    Google Scholar 

  4. Ash, A.: Cohomology of congruence subgroups of SL(n,ℤ). Math. Ann.249, 55–73 (1980)

    Google Scholar 

  5. Ash, A.: Small-dimensional classifying spaces for subgroups of general linear groups. Duke Math. J.51, 459–468 (1984)

    Google Scholar 

  6. Barnes, E.S.: The complete enumeration of extreme senary forms. Philos. Trans. R. Soc. Lond. A249, 461–506 (1957)

    Google Scholar 

  7. Bourbaki, N.: Groupes et algèbres de Lie, Chap. III. In: Elém. Math.37, 1349 (1972)

  8. Conway, J.H., Sloane, N.J.A.: Sphere packings, lattices and groups. Berlin Heidelberg New York: Springer 1988

    Google Scholar 

  9. Coxeter, H.S.M.: Extreme forms. Can. J. Math.3, 391–441 (1951)

    Google Scholar 

  10. Goresky, M., MacPherson, R.: Stratified Morse theory (the book). Berlin Heidelberg New York: Springer 1988

    Google Scholar 

  11. Hartshorne, R.: Foundations of projective geometry. Reading, Mass.: Benjamin/Cummings 1967

    Google Scholar 

  12. Jacobson, N.: Basic algebra I. San Francisco: Freeman 1974

    Google Scholar 

  13. Lee, R., Szczarba, R.H.: On the homology and cohomology of congruence subgroups. Invent. Math.33, 15–53 (1976)

    Google Scholar 

  14. Lee, R., Szczarba, R.H.: On the torsion inK 4(ℤ) andK 5(ℤ). Duke Math. J.45, 101–129 (1978)

    Google Scholar 

  15. MacPherson, R., McConnell, M.: Classical projective geometry and modular varieties. In: Algebraic analysis, geometry, and number theory. Proceedings of the JAMI Inaugural conference. Igusa, J.-I. (ed.) Baltimore: J. Hopkins Univ. Press 1989

    Google Scholar 

  16. MacPherson, R., McConnell, M.: Explicit reduction theory for Sp (4,ℤ) (to appear)

  17. Namikawa, Y.: Toroidal compactifications of Siegel spaces. (Lect. Notes Math., vol. 812) Berlin Heidelberg New York: Springer 1980

    Google Scholar 

  18. Serre, J.-P.: Arithmetic groups. In: Homological group theory. London Math. Soc. Lecture Note Ser. 36, ed. by Wall, C.T.C., Cambridge Univ. Press, Cambridge, 1979, pp. 105–136

    Google Scholar 

  19. Soulé, C.: The cohomology of SL(3,ℤ). Topology17, 1–22 (1978)

    Google Scholar 

  20. Soulé, C.: Thèse, Univ. Paris VII (1979)

  21. Štogrin, M.I.: Locally quasi-densest lattice packings of spheres. Soviet Math. Doklady15, 1288–1292 (1974)

    Google Scholar 

  22. Voronoi, G.: Sur quelques propriétés des formes quadratiques positives parfaites. Crelle133, 97–178 (1908)

    Google Scholar 

  23. Voronoi, G.: Recherches sur les paralléloèdres primitifs. Crelle134, 198–287 (1980)

    Google Scholar 

  24. Voronoi, G.: Domaines de formes quadratiques correspondant aux différents types de paralléloèdres primitifs. Crelle136, 67–181 (1909)

    Google Scholar 

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Partially supported by NSF grant DMS-8715305

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McConnell, M. Classical projective geometry and arithmetic groups. Math. Ann. 290, 441–462 (1991). https://doi.org/10.1007/BF01459253

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