Infinitesimal computations in topology. (English) Zbl 0374.57002


57R55 Differentiable structures in differential topology
57M10 Covering spaces and low-dimensional topology
57R65 Surgery and handlebodies
58A10 Differential forms in global analysis
Full Text: DOI Numdam EuDML


[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. · Zbl 0052.40001
[2] R. Body andR. Douglas, Homotopy types within a rational homotopy type,Topology,13 (1974), 209–214. · Zbl 0299.55008
[3] A. Borel andHarish-Chandra, Arithmetic Subgroups of Algebraic Groups,Ann. of Math.,75 (1962), 485–535. · Zbl 0107.14804
[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.
[7] Elie Cartan, Sur les nombres de Betti des espaces de groupes clos,C. R. Acad. Sci., Paris,187 (1928), 196–198. · JFM 54.0604.01
[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. · JFM 55.0228.01
[10] M. Gromov, Homotopical effects of Dilatation, submitted toJournal of Diff. Geom. · Zbl 0427.58010
[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. · Zbl 0041.52002
[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. · Zbl 0321.13011
[13] Daniel M. Kan, A Combinatorial definition of homotopy groups,Annals of Math.,67 (1958), 282–312. · Zbl 0091.36901
[14] M. Kervaire andJ. Milnor, Groups of homotopy spheres I,Ann. of Math.,77 (1963), 504–557. · Zbl 0115.40505
[15] R. C. Kirby andL. C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung,Bull. Amer. Math. Soc.,75 (1969), 742–749. · Zbl 0189.54701
[16] J. Milnor, Geometric realization of a semi-simplicial complex,Ann. of Math.,65 (1957), 357–362. · Zbl 0078.36602
[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. · Zbl 0118.18601
[18] G. D. Mostow, Fully Reducible Subgroups of Algebraic Groups,Amer. J. Math.,78 (1956), 200–221. · Zbl 0073.01603
[19] S. P. Novikov, Homotopically Equivalent Smooth Manifolds,AMS Translations (2),48 (1965), 271–396.
[20] HenriPoincaré, Analysis situs,OEuvres, 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. · Zbl 0191.53702
[22] Jean-Pierre Serre, Homologie singulière des espaces fibrés. Applications,Ann. of Math.,54 (1951), 425–505. · Zbl 0045.26003
[23] Jean-Pierre Serre, Cohomologie galoisienne,Lecture Notes in Math., no 3, Berlin, Springer, 1973. · Zbl 0259.12011
[24] R. E. Stong, Relations among characteristic Numbers I,Topology,4 (1965), 267–281; II,ibid.,5 (1966), 133–148. · Zbl 0136.20503
[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. · Zbl 0355.57007
[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.
[29] Dennis Sullivan, On the intersection ring of compact three manifolds,Topology,14 (1975), 275–277. · Zbl 0312.57003
[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.
[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. · Zbl 0084.39202
[35] C. T. C.Wall,Surgery on compact manifolds, Academic Press, 1970.
[36] A. Weil,Variétés Kähleriennes, Paris, Hermann, 1958.
[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. · Zbl 0030.07902
[39] H. Whitney,Geometric Integration Theory, Princeton University Press, 1957. · Zbl 0083.28204
[40] Wu Wen Tsün, Theory of I* Functor in Algebraic Topology,Scientia Sinica, Vol. XVIII and Vol. XII. · Zbl 0348.55010
[41] P. Deligne andD. Sullivan, Fibrés vectoriels complexes à groupe structural discret,C. R. Acad. Sc. Paris,281 (1975), 1081–1083. · Zbl 0317.55016
[42] P. Deligne, P. Griffiths, J. Morgan, D. Sullivan, The real homotopy of Kaehler manifolds,Invent. Math.,29 (1975), 245–274. · Zbl 0312.55011
[43] D. Sullivan, M. Vigué, The homology theory of the closed geodesic problem,Journal of Diff. Geom.,11 (1976), 633–644. · Zbl 0361.53058
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.