La dichotomie elliptique - Hyperbolique en homotopie rationnelle
Astérisque, no. 176 (1989), 189 p.
@book{AST_1989__176__1_0,
     author = {F\'elix, Yves},
     title = {La dichotomie elliptique - Hyperbolique en homotopie rationnelle},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {176},
     year = {1989},
     zbl = {0691.55001},
     mrnumber = {1035582},
     language = {fr},
     url = {http://www.numdam.org/item/AST_1989__176__1_0}
}
Félix, Yves. La dichotomie elliptique - Hyperbolique en homotopie rationnelle. Astérisque, no. 176 (1989), 189 p. http://www.numdam.org/item/AST_1989__176__1_0/

[1] J. F. Adams - On the cobar construction. Proc. N.A.S. U.S.A. 42 (1956), 409-412. | Article | MR 79266 | Zbl 0071.16404

[2] J. F. Adams et P. Hilton - On the chain algebra of a loop space. Comment. Math. Helv. 30 (1955), 305-330. | Article | MR 77929 | Zbl 0071.16403

[3] P. Andrews et M. Arkowitz - Sullivan's minimal models and higher order Whitehead products. Can. J. of Math. 30-5 (1978), 961-982. | Article | MR 506254 | Zbl 0441.55012

[4] D. Anick - The smallest Ω-irrational CW complex. J. of pure and applied algebra 28 (1983), 213-222. | Article | MR 701349 | Zbl 0582.55009

[5] D. Anick - Homotopy exponents for spaces of category two. Preprint (1987). | MR 1000365 | Zbl 0671.55009

[6] D. Anick - A loop space whose homology has torsion of all orders. Pacific Journal of Mathematics 123 (1986), 257-262. | Article | MR 840843 | Zbl 0553.55005

[7] M. Aubry et J. M. Lemaire - Zero divisors in enveloping algebras of graded Lie algebras. J. of pure and applied algebra 38 (1985), 159-166. | Article | MR 814174 | Zbl 0587.55006

[8] L. Avramov - Torsion in loop space homology. Topology 25 (1986), 155-157 | Article | MR 837618 | Zbl 0594.55007

[9] I. Babenko - On analytical properties of Poincaré series of loop spaces. Math. Zam 27 (1980), 751-764. | MR 578259 | Zbl 0455.55006

[10] J. Backelin - Monomial ideal residue class rings and iterated Golod maps. Math. Scand. 53 (1983), 16-24. | Article | MR 733934 | Zbl 0557.13012

[11] H. Baues et J. M. Lemaire - Minimal models in homotopy theory. Math. Ann. 225-3 (1977), 219-242. | Article | MR 431172 | Zbl 0322.55019

[12] I. Berstein et T. Ganea - The category of a map and of a cohomology class. Fundam. Math. 50 (1961/2), 265-279. | Article | MR 139168 | Zbl 0192.29302

[13] J. E. Bjork - Rings of differential operators. North-Holland, vol. 21, (1979). | Zbl 0499.13009

[14] R. Body et D. Sullivan - Homotopy types with telescope. Preprint U.C.S.D. La Jolla, California.

[15] R. Bogvad - Some elementary results on the cohomology of graded Lie algebras. S.M.F. Astérisque 113-114 (1984), 156-166. | Numdam | Zbl 0552.17012

R. Bogvad - Some elementary results on the cohomology of graded Lie algebras. Homotopie algebrique et algèbre locale. Luminy (1982). | Numdam | Zbl 0552.17012

[16] R. Bogvad - The enveloping algebra of a graded Lie algebra of global dimension two contains a free subalgebra on two generators. J. of pure and applied algebra 38 (1985), 213-216. | Article | Zbl 0587.55004

[17] R. Bogvad et S. Halperin - On a conjecture of Roos. Lecture Notes in Math. 1183 (1985), 120-127. | Zbl 0644.13004

R. Bogvad et S. Halperin - On a conjecture of Roos. Nordic summer school on relations between algebraic topology and local rings, 1983, Stockholm. | Zbl 0644.13004

[18] R. Bogvad et C. Jacobsson - Graded Lie algebras of depth one. Report 3 (1989) department of mathematics, University of Stockholm. | Zbl 0692.55007

[19] 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 | Zbl 0052.40001

[20] A. K. Bousfield et V. K. A. M. Gugenheim - On P.L. de Rham theory and rational homotopy type. Memoir of the A.M.S. 179 (1976). | Zbl 0338.55008

[21] A. K. Bousfield et D. M. Kan - Homotopy limits, completions and localizations. Lecture Notes in mathematics n 304 (1972), Springer Verlag. | Zbl 0259.55004

[22] H. Cartan - Cohomologie des Kπ,n. Séminaire Cartan 1954/1955, exposés 9 et 10. Paris, (1956).

[23] H. Cartan - La transgression dans un groupe de Lie et dans un fibré principal. Colloque de topologie, Bruxelles (1950). | Zbl 0045.30701

[24] B. Cenkl et R. Porter - Malcev's completion of a group and differential forms. J. of dif. geometry, 15 (1980), 531-542. | Article | Zbl 0491.20033

[25] P. Deligne, P. Griffiths, J. Morgan et D. Sullivan - The real homotopy theory of Kähler manifolds. Invent. Math. 29 (1975), 245-254. | Article | Zbl 0312.55011

[26] G. L. Feld'Man - Ends of Lie algebras. Uspekhi Math. Nauk. 38 (1983), 199-200. | Zbl 0534.17007

[27] Y. Félix - Caractéristique d'Euler homotopique. C.R.A.S. Paris 291 (1980). | Zbl 0459.55005

[28] Y. Félix - Dénombrement des types de k-homotopie. Théorie de la déformation. Mémoire de la S.M.F., 3 (1980). | Numdam | Zbl 0452.55005

[29] Y. Félix - Catégorie L.S. et invariant e. S.M.F. Astérisque 113-114 (1984), 179-182. | Numdam | Zbl 0547.55007

Y. Félix - Catégorie L.S. et invariant e. Homotopie algébrique et algèbre locale. Luminy, 1982. | Numdam | Zbl 0547.55007

[30] Y. Félix et S. Halperin - Rational L.S. category and its applications. T.A.M.S. 273 (1982), 1-37. | Article | Zbl 0508.55004

[31] Y. Félix et S. Halperin - Formal spaces with finite dimensional rational homotopy. T.A.M.S. 270 (1982), 575-588. | Article | Zbl 0489.55009

[32] Y. Félix, S. Halperin, C. Jacobson, C. Lofwall et J. C. Thomas - The radical of the homotopy Lie algebra. Amer. J. of Math. (1988), 301-322. | Article | Zbl 0654.55011

[33] Y. Félix, S. Halperin, J. M. Lemaire et J. C. Thomas - Mod p loop space homology. Invent. Math. 95 (1989), 247-262. | Article | Zbl 0667.55007

[34] Y. Félix, S. Halperin, D. Tanré et J. C. Thomas - The radical of π*ΩS𝐐. Lecture Notes in Math. 1183 (1986), 133-135. | Zbl 0612.55015

[35] Y. Félix, S. Halperin et J. C. Thomas - The homotopy Lie algebra for finite complexes. Publ. I.H.E.S. 56 (1982), 179-202. | Numdam | Zbl 0504.55005

[36] Y. Félix, S. Halperin et J. C. Thomas - L.S. catégorie et suite spectrale de Milnor-Moore. Bull. S.M.F. 111 (1983), 89-96. | Numdam | Zbl 0538.55007

[37] Y. Félix, S. Halperin et J. C. Thomas - Hopf algebras of polynomial growth. A paraître Journal of Algebra. | Zbl 0676.16008

[38] Y. Félix, S. Halperin et J. C. Thomas - Loop space homology of spaces of L.S. category one and two. Preprint. | Zbl 0687.55004

[39] Y. Félix, S. Halperin et J. C. Thomas - The grade of a fìbration. Preprint.

[40] Y. Félix, S. Halperin et J. C. Thomas - Engel's elements in the homotopy Lie algebra. Preprint. | Zbl 0737.17011

[41] Y. Félix et J. M. Lemaire - On the mapping theorem for L.S. category. Topology 24 (1985), 41-43. | Article | Zbl 0572.55002

[42] Y. Félix et J. M. Lemaire - On the mapping theorem for L.S. category II. A paraître Can J. of Math.

[43] Y. Félix et J. C. Thomas - The radius of convergence of Poincaré series of loop spaces. Invent. Math. 68 (1982), 257-274. | Article | Zbl 0476.55016

[44] Y. Félix et J. C. Thomas - Sur l'opération d'holonomie rationnelle. Lecture Notes in Math. 1183 (1986), 136-169. | Zbl 0594.55011

[45] Y. Félix et J. C. Thomas - On the ubiquity of the rational homotopy Lie algebra of a topological space. Bull Soc. Math. Belgique 38 (1986), 175-190. | Zbl 0637.55005

[46] Y. Félix et J. C. Thomas - Sur la structure des espaces de L.S. catégorie deux. Illinois J. of Math. 30 (1986), 574-593. | Zbl 0585.55010

[47] J. Friedlander et S. Halperin - An arithmetic characterization of the rational homotopy group of certain spaces. Invent. Math. 53 (1979), 117-138. | Article | Zbl 0396.55010

[48] T. Ganea - Lusternik-Schnirelmann category and strong category. Illinois J. Math. 11 (1967), 417-427. | Zbl 0149.40703

[49] W. Gilbert - Some examples for weak category and conilpotency. Illinois J. Math. 12 (1968), 421-432. | Zbl 0157.54203

[50] W. Gilbert - Some problems in algebraic topology on Lusternik-Schnirelmann categories and cocategories. Thesis (1967), Oxford.

[51] M. Ginsburg - On the Lusternik-Schnirelmann category. Ann. Math. 77 (1963), 538-551. | Article | Zbl 0148.17003

[52] L. V. Goncharova - Cohomology of Lie algebras of formal vector fields on the line. Funkt. Anal. 7 (1973), 6-14. | Zbl 0284.17006

[53] D. H. Gottlieb - Evaluation subgroup of homotopy groups. Amer. J. Math. 91 (1969), 729-756. | Article | Zbl 0185.27102

[54] W. Greub, S. Halperin et Vanstone - Connections, curvature and cohomology III. Academic press, New York, (1976). | Zbl 0372.57001

[55] P. A. Griffiths et J. W. Morgan - Rational homotopy theory and differential forms. Progress in Math. 16, Birkhaüser (1981). | Zbl 0474.55001

[56] D. Gromoll et W. Meyer - Periodic geodesics on compact riemannian manifolds. J. Diff. Geom. 3 (1969), 493-500. | Article | Zbl 0203.54401

[57] D. Gromov - Curvature, diameter and Betti numbers. Comment. Math. Helv. 56 (1981), 179-195. | Article | Zbl 0467.53021

[58] K. Grove et S. Halperin - Contributions of rational homotopy to global problems in geometry. Publ. I.H.E.S. 56 (1982), 171-177. | Numdam | Zbl 0508.55013

[59] S. Halperin - Finiteness in the minimal models of Sullivan. T.A.M.S. 230 (1977), 173-199. | Article | Zbl 0364.55014

[60] S. Halperin - Lectures on minimal models. Memoire S.M.F. 9-10 (1983). | Numdam | Zbl 0536.55003

[61] S. Halperin - Spaces whose rational homology and ψ -homotopy are both finite dimensional. S.M.F. Astérisque 113-114 (1984), 198-205. | Numdam | Zbl 0546.55015

S. Halperin - Spaces whose rational homology and ψ -homotopy are both finite dimensional. Homotopie algébrique et algèbre locale. Luminy, 1982. | Numdam | Zbl 0546.55015

[62] S. Halperin et G. Levin - High skeleta of CW complexes. Lecture Notes in Math. 1183 (1986), 211-217. | Zbl 0607.55006

S. Halperin et G. Levin - High skeleta of CW complexes. Nordic summer school on relations between algebraic topology and local rings, 1983, Stockholm. | Zbl 0607.55006

[63] S. Halperin et J. Stasheff - Obstructions to homotopy equivalences. Advances in Math. 32 (1979), 233-279. | Article | Zbl 0408.55009

[64] K. A. Hardie - A note on fìbrations and category. Michigan Math. J. 17 (1970), 351-352. | Article | Zbl 0185.51103

[65] K. A. Hardie - An upper bound for cat E. Bull. London Math. Soc. 17 (1985), 395-396. | Article | Zbl 0578.55003

[66] H. W. Henn - On almost rational co-H-spaces. Proc. A.M.S. 87 (1983), 164-168. | Zbl 0513.55008

[67] P. Hilton, G. Mislin et J. Roitberg - Localization of nilpotent groups and spaces. Math. studies (North Holland) 15 (1975). | Zbl 0323.55016

[68] G. P. Hochschild et J. P. Serre - Cohomology of Lie algebras. Ann. Math. 57, n 3, (1953), 591-603. | Article | Zbl 0053.01402

[69] I. James - On category, in the sense of Lusternik-Schnirelmann. Topology 17 (1978), 331-348. | Article | Zbl 0408.55008

[70] J. L. Koszul - Homologie et cohomologie des algèbres de Lie. Bull. S.M.F. 78 (1950), 65-127. | Numdam | Zbl 0039.02901

[71] G. R. Krause et T. H. Lenagan - Growth of algebras and Gelfand-Kirillov dimension. Pitman (1985). | Zbl 0564.16001

[72] J. Lannes et L. Schwartz - A propos de conjectures de Serre et Sullivan. Invent. Math. 83 (1986), 596-603. | Article | Zbl 0563.55011

[73] D. Lehmann- Théorie homotopique des formes différentielles. S.M.F. Astérisque 45 (1977). | Zbl 0367.55008

[74] J. M. Lemaire - A finite complex, whose rational homotopy is not finitely generated. Lecture Notes in Math. 196 (1971), 114-120. | Zbl 0216.44905

[75] J. M. Lemaire - Algèbres connexes et homologie des espaces de lacets. Lecture Notes in Math. 422 (1974). | Zbl 0293.55004

[76] J. M. Lemaire - Lusternik-Schnirelmann category : an introduction. Lecture Notes in Math. 1183 (1986), 259-276. | Zbl 0594.55012

J. M. Lemaire - Lusternik-Schnirelmann category : an introduction. Nordic summer school on relations between Algebraic topology and local rings, 1983, Stockholm. | Zbl 0594.55012

[77] J. M. Lemaire et F. Sigrist - Sur les invariants d'homotopie rationnelle liés à la L.S. catégorie. Comment. Math. Helv. 56 (1981), 103-122. | Article | Zbl 0479.55008

[78] C. Lofwall et J. E. Roos - Cohomologie des algèbres de Lie graduées et séries de Poincaré-Betti non rationnelles. Notes C.R.A.S. Paris 290 (1980), 733-736. | Zbl 0449.13011

[79] C. Macgibbon et C. W. Wilkerson - Loop spaces of finite complexes at large primes. Preprint. | Article | Zbl 0594.55006

[80] H. Matsumura - Commutative algebra. (1980), Benjamin. | Zbl 0441.13001

[81] J. W. Milnor - Construction of universal bundles II. Ann of Math. 63 (1956) 430-436. | Article | Zbl 0071.17401

[82] J. W. Milnor et J. C. Moore - On the structure of Hopf algebras. Ann. of Math. 81 (1965), 211-264. | Article | Zbl 0163.28202

[83] C. Nastasescu et F. Van Oystaeyen - Dimensions of ring theory (1987), Reidel Publishing Company. | Zbl 0626.16001

[84] J. Neisendorfer - Lie algebras, coalgebras and rational homotopy theory for nilpotent spaces. Pacific Journal of Mathematics 74 (1978), 429-460. | Article | Zbl 0386.55016

[85] J. Neisendorfer et P. S. Selick - Some examples of spaces with or without exponents. Can Math. Soc. Conf. Proc. Vol. 2, part. 1 (1982). | Zbl 0551.55009

[86] D. Quillen - Rational homotopy theory. Ann. of Math. 90 (1969), 205-295. | Article | Zbl 0191.53702

[87] J. E. Roos - On the use of graded Lie algebras in the theory of local rings. London Math. Soc. Lecture notes series, 72 (1982) 204-230, Cambridge University Press. | Zbl 0523.13010

[88] H. Sheerer - Fibrewise P-universal nilpotent fibration. Proc. Royal Soc. Edinburgh 98 (1984), 89-104. | Article | Zbl 0561.55011

[89] P. S. Selick - Moore conjectures. Lecture Notes in Math. 1318 (1988). 219-227. | Zbl 0665.55008

[90] J. P. Serre - Groupes d'homotopie et classes de groupes abéliens. Ann. of math. 58 (1953), 258-294. | Article | Zbl 0052.19303

[91] W. Smoke - Dimension and multiplicity for graded algebras. J. of algebra 21, (1972), 149-173. | Article | Zbl 0231.13006

[92] E. H. Spanier - Algebraic topology. Mac Graw Hill. Academic Press (1966). | Zbl 0145.43303

[93] D. Sullivan - Infinitesimal computations in topology. Publ. I.H.E.S. 47 (1977), 269-331. | Article | Numdam | Zbl 0374.57002

[94] D. Sullivan et M. Vigué-Poirrier - The homology theory of the closed geodesic problem. J. of Dif. Geometry 11 (1976), 633-644. | Article | Zbl 0361.53058

[95] D. Tanré - Homotopie rationnelle : Modèles de Chen, Quillen, Sullivan. Lecture Notes in Math. 1025 (1983). | Zbl 0539.55001

[96] D. Tanré - Cohomologie de Harrison et espaces projectifs tronqués. Journal of Pure and Applied Algebra 38 (1985), 355-366. | Article | Zbl 0587.55003

[97] R. Thom - Operations en cohomoîogie réelle. Séminaire Cartan 1955, exposé 17. | Numdam

[98] G. H. Toomer - L.S. category and the Moore spectral sequence. Math. Z. 138 (1974), 123-143. | Article | Zbl 0284.55012

[99] G. Whitehead - The homology suspension. Colloque de Topologie algébrique. Louvain 1956, 89-95. | Zbl 0079.39101

[100] O. Zariski et P. Samuel- Commutative algebra vol. II. Graduate texts in mathematics n° 29, Springer Verlag. | Zbl 0322.13001