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Infinitesimal computations in topology

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Bibliography

  1. A. Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts,Ann. of Math.,57 (1953), 115–207.

    Article  MathSciNet  Google Scholar 

  2. R. Body andR. Douglas, Homotopy types within a rational homotopy type,Topology,13 (1974), 209–214.

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Borel andHarish-Chandra, Arithmetic Subgroups of Algebraic Groups,Ann. of Math.,75 (1962), 485–535.

    Article  MathSciNet  Google Scholar 

  4. Wm.Browder,Surgery on simply connected manifolds, Springer Ergebnisse Series, 1971.

  5. R. Body andD. Sullivan, Zariski Dynamics of a Homotopy Type, to be submitted toTopology (preprint, UCSD La Jolla, California).

  6. O. Burlet, Rational Homotopy of oriented Thom Spaces,Proceedings of the Advanced Study Institute on algebraic topology Aarhus (1970), vol.1, 20–22.

    MathSciNet  Google Scholar 

  7. Elie Cartan, Sur les nombres de Betti des espaces de groupes clos,C. R. Acad. Sci., Paris,187 (1928), 196–198.

    Google Scholar 

  8. HenriCartan, La transgression dans un groupe de Lie et dans un espace fibré principal, Notions d’algèbre différentielle : application aux groupes de Lie et aux variétés où opère un groupe de Lie,Colloque de topologie (espaces fibrés), 58–71, Bruxelles, 1950.

  9. G. De Rham, Intégrales multiples et Analysis Situs,C. R. Acad. Sci. Paris,188 (1929), 1651–1652.

    MATH  Google Scholar 

  10. M. Gromov, Homotopical effects of Dilatation, submitted toJournal of Diff. Geom.

  11. Guy Hirsch, Sur la structure multiplicative de l’anneau de cohomologie d’un espace fibré,C. R. Acad. Sci. Paris,230 (1950), 46–48.

    MATH  MathSciNet  Google Scholar 

  12. M. C. Heydemann andM. Vigué, Application de la théorie des polynômes de Hilbert-Samuel à l’étude de certaines algèbres différentielles,C. R. Acad. Sci. Paris,278 (1974), A, 1607–1610.

    MATH  Google Scholar 

  13. Daniel M. Kan, A Combinatorial definition of homotopy groups,Annals of Math.,67 (1958), 282–312.

    Article  MathSciNet  Google Scholar 

  14. M. Kervaire andJ. Milnor, Groups of homotopy spheres I,Ann. of Math.,77 (1963), 504–557.

    Article  MathSciNet  Google Scholar 

  15. R. C. Kirby andL. C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung,Bull. Amer. Math. Soc.,75 (1969), 742–749.

    Article  MATH  MathSciNet  Google Scholar 

  16. J. Milnor, Geometric realization of a semi-simplicial complex,Ann. of Math.,65 (1957), 357–362.

    Article  MathSciNet  Google Scholar 

  17. J. Milnor, A procedure for killing the homotopy groups of a differentiable manifold,Proc. Sympos. Pure Math. III, Amer. Math. Soc., 1961, 39–55.

  18. G. D. Mostow, Fully Reducible Subgroups of Algebraic Groups,Amer. J. Math.,78 (1956), 200–221.

    Article  MATH  MathSciNet  Google Scholar 

  19. S. P. Novikov, Homotopically Equivalent Smooth Manifolds,AMS Translations (2),48 (1965), 271–396.

    Google Scholar 

  20. HenriPoincaré, Analysis situs,Œuvres, t. VI, 193–288, alsoJournal de l’Ecole Polytechnique (2),1 (1895), 1–123.

  21. Daniel Quillen, Rational Homotopy Theory,Ann. of Math.,90 (1969), 205–295.

    Article  MathSciNet  Google Scholar 

  22. Jean-Pierre Serre, Homologie singulière des espaces fibrés. Applications,Ann. of Math.,54 (1951), 425–505.

    Article  MathSciNet  Google Scholar 

  23. Jean-Pierre Serre, Cohomologie galoisienne,Lecture Notes in Math., no 3, Berlin, Springer, 1973.

    MATH  Google Scholar 

  24. R. E. Stong, Relations among characteristic Numbers I,Topology,4 (1965), 267–281; II,ibid.,5 (1966), 133–148.

    Article  MATH  MathSciNet  Google Scholar 

  25. DennisSullivan, Differential forms and the topology of manifolds,Manifolds-Tokyo (1973) (Proc. of the Intern. Conf. on Manifolds and related topics in Topology, Tokyo 1973) (ed. A. Hattori), U. of Tokyo Press, 1975, 37–49.

  26. Dennis Sullivan, Genetics of Homotopy Theory and the Adams Conjecture,Annals of Math.,100 (1974), 1–79.

    Article  MathSciNet  Google Scholar 

  27. DennisSullivan,Triangulating homotopy equivalences, Thesis, Princeton University (1966).

  28. Dennis Sullivan, Geometric periodicity and the invariants of manifolds,Manifolds-Amsterdam (1970) (Proc. of the Nuffic Summer School on Manifolds, Amsterdam 1970) (ed. N. Kuiper),Lecture Notes in Math., no 197, Berlin, Springer, 1971.

    Google Scholar 

  29. Dennis Sullivan, On the intersection ring of compact three manifolds,Topology,14 (1975), 275–277.

    Article  MATH  MathSciNet  Google Scholar 

  30. DennisSullivan, Inside and Outside manifolds,Proc. Intern. Cong. of Math., Vancouver, 1974, 201–207.

  31. Dennis Sullivan, Galois symmetry in manifold theory at the primes,Actes du Congrès intern. des Math., Nice (1970), vol. 2, 169–175, Paris, Gauthier-Villars, 1971.

    Google Scholar 

  32. RenéThom, Les classes caractéristiques de Pontryagin des variétés triangulées,Symposium international de topologia algebraica, 54–67, Mexico, 1958.

  33. RenéThom,Opérations en cohomologie réelle, Séminaire H. Cartan, 1954–55, Exposé 17.

  34. N. T. Van Est, A generalization of the Cartan Leray spectral sequence,Proc. Koninkl. Ned. Akad., série A, 1958, p. 399–413.

  35. C. T. C.Wall,Surgery on compact manifolds, Academic Press, 1970.

  36. A. Weil,Variétés Kähleriennes, Paris, Hermann, 1958.

    MATH  Google Scholar 

  37. J. H. C. Whitehead, Certain equations in the algebra of a semi-simple infinitesimal group,Math. works, vol.I, 291–308 (see alsoThe works of J. H. C. Whitehead by JohnMilnor,ibid., XXII–XXXIII).

  38. J. H. C. Whitehead, An expression of the Hopf invariant as an integral,Proc. Nat. Acad. Sci. U.S.A.,33 (1947), 117–123 =Math. Works, vol.I, 317–323.

    Article  MATH  MathSciNet  Google Scholar 

  39. H. Whitney,Geometric Integration Theory, Princeton University Press, 1957.

  40. Wu Wen Tsün, Theory of I* Functor in Algebraic Topology,Scientia Sinica, Vol. XVIII and Vol. XII.

  41. P. Deligne andD. Sullivan, Fibrés vectoriels complexes à groupe structural discret,C. R. Acad. Sc. Paris,281 (1975), 1081–1083.

    MATH  MathSciNet  Google Scholar 

  42. P. Deligne, P. Griffiths, J. Morgan, D. Sullivan, The real homotopy of Kaehler manifolds,Invent. Math.,29 (1975), 245–274.

    Article  MATH  MathSciNet  Google Scholar 

  43. D. Sullivan, M. Vigué, The homology theory of the closed geodesic problem,Journal of Diff. Geom.,11 (1976), 633–644.

    MATH  Google Scholar 

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Sullivan, D. Infinitesimal computations in topology. Publications Mathématiques de L’Institut des Hautes Scientifiques 47, 269–331 (1977). https://doi.org/10.1007/BF02684341

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