Infinitesimal computations in topology

Sullivan, Dennis

Publications Mathématiques de l'IHÉS, Tome 47 (1977), pp. 269-331.

[B] 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. | MR | Zbl

[BD] R. Body and R. Douglas, Homotopy types within a rational homotopy type, Topology, 13 (1974), 209-214. | MR | Zbl

[B-HC] A. Borel and Harish-Chandra, Arithmetic Subgroups of Algebraic Groups, Ann. of Math., 75 (1962), 485-535. | MR | Zbl

[Br] Wm. Browder, Surgery on simply connected manifolds, Springer Ergebnisse Series, 1971.

[BS] R. Body and D. Sullivan, Zariski Dynamics of a Homotopy Type, to be submitted to Topology (preprint, UCSD La Jolla, California).

[Bu] O. Burlet, Rational Homotopy of oriented Thom Spaces, Proceedings of the Advanced Study Institute on algebraic topology Aarhus (1970), vol. 1, 20-22. | MR

[C] Elie Cartan, Sur les nombres de Betti des espaces de groupes clos, C. R. Acad. Sci., Paris, 187 (1928), 196-198. | JFM

[C] Henri Cartan, 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. | Zbl

[D] G. De Rham, Intégrales multiples et Analysis Situs, C. R. Acad. Sci. Paris, 188 (1929), 1651-1652. | JFM

[Gr] M. Gromov, Homotopical effects of Dilatation, submitted to Journal of Diff. Geom. | Zbl

[H] Guy Hirsch, Sur la structure multiplicative de l'anneau de cohomologie d'un espace fibré, C. R. Acad. Sci. Paris, 230 (1950), 46-48. | Zbl

[H-V] M. C. Heydemann and M. 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. | Zbl

[K] Daniel M. Kan, A Combinatorial definition of homotopy groups, Annals of Math., 67 (1958), 282-312. | MR | Zbl

[KM] M. Kervaire and J. Milnor, Groups of homotopy spheres I, Ann. of Math., 77 (1963), 504-557. | MR | Zbl

[KS] R. C. Kirby and L. C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc., 75 (1969), 742-749. | MR | Zbl

[M1] J. Milnor, Geometric realization of a semi-simplicial complex, Ann. of Math., 65 (1957), 357-362. | MR | Zbl

[M2] J. Milnor, A procedure for killing the homotopy groups of a differentiable manifold, Proc. Sympos. Pure Math. III, Amer. Math. Soc., 1961, 39-55. | MR | Zbl

[Mo] G. D. Mostow, Fully Reducible Subgroups of Algebraic Groups, Amer. J. Math., 78 (1956), 200-221. | MR | Zbl

[N] S. P. Novikov, Homotopically Equivalent Smooth Manifolds, AMS Translations (2), 48 (1965), 271-396.

[P] Henri Poincaré, Analysis situs, Oeuvres, t. VI, 193-288, also Journal de l'Ecole Polytechnique (2), 1 (1895), 1-123. | JFM

[Q] Daniel Quillen, Rational Homotopy Theory, Ann. of Math., 90 (1969), 205-295. | MR | Zbl

[Se1] Jean-Pierre Serre, Homologie singulière des espaces fibrés. Applications, Ann. of Math., 54 (1951), 425-505. | MR | Zbl

[Se2] Jean-Pierre Serre, Cohomologie galoisienne, Lecture Notes in Math., n° 3, Berlin, Springer, 1973.

[St] R. E. Stong, Relations among characteristic Numbers I, Topology, 4 (1965), 267-281 ; II, ibid., 5 (1966), 133-148. | Zbl

[Su1] Dennis Sullivan, 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. | Zbl

[Su2] Dennis Sullivan, Genetics of Homotopy Theory and the Adams Conjecture, Annals of Math., 100 (1974), 1-79. | MR | Zbl

[Su3] Dennis Sullivan, Triangulating homotopy equivalences, Thesis, Princeton University (1966).

[Su4] 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., n° 197, Berlin, Springer, 1971. | Zbl

[Su5] Dennis Sullivan, On the intersection ring of compact three manifolds, Topology, 14 (1975), 275-277. | MR | Zbl

[Su6] Dennis Sullivan, Inside and Outside manifolds, Proc. Intern. Cong. of Math., Vancouver, 1974, 201-207. | Zbl

[Su7] 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. | Zbl

[T] René Thom, Les classes caractéristiques de Pontryagin des variétés triangulées, Symposium internacional de topologia algebraica, 54-67, Mexico, 1958. | Zbl

[TC] René Thom, Opérations en cohomologie réelle, Séminaire H. Cartan, 1954-1955, Exposé 17. | Numdam

[VE] N. T. Van Est, A generalization of the Cartan Leray spectral sequence, Proc. Koninkl. Ned. Akad., série A, 1958, p. 399-413. | MR | Zbl

[Wa] C. T. C. Wall, Surgery on compact manifolds, Academic Press, 1970. | MR | Zbl

[We] A. Weil, Variétés Kähleriennes, Paris, Hermann, 1958. | Zbl

[Wh1] J. H. C. Whitehead, Certain equations in the algebra of a semi-simple infinitesimal group, Math. works, vol. I, 291-308 (see also The works of J. H. C. Whitehead by John MILNOR, ibid., XXII-XXXIII).

[Wh2] 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. | MR | Zbl

[W] H. Whitney, Geometric Integration Theory, Princeton University Press, 1957. | MR | Zbl

[Wu] Wu Wen Tsün, Theory of I* Functor in Algebraic Topology, Scientia Sinica, Vol. XVIII and Vol. XII. | Zbl

[DS] P. Deligne and D. Sullivan, Fibrés vectoriels complexes à groupe structural discret, C. R. Acad. Sc. Paris, 281 (1975), 1081-1083. | MR | Zbl

[DGMS] P. Deligne, P. Griffiths, J. Morgan, D. Sullivan, The real homotopy of Kaehler manifolds, Invent. Math., 29 (1975), 245-274. | MR | Zbl

[SV] D. Sullivan, M. Vigué, The homology theory of the closed geodesic problem, Journal of Diff. Geom., 11 (1976), 633-644. | MR | Zbl