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The radius of convergence of Poincaré series of loop spaces. (English) Zbl 0476.55016


MSC:

55P62 Rational homotopy theory
55P35 Loop spaces
16W50 Graded rings and modules (associative rings and algebras)
55M30 Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects)
14M10 Complete intersections
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References:

[1] Avramov, L.: On the convergence radius of Poincaré series of local rings. Reports no 4 (1979). Dept. of Math. Univ. of Stokholm · Zbl 0433.13010
[2] Avramov, L.: Sur la croissance des nombres de Betti d’un anneau local. Notes aux C.R.A.S.289, 369-372 (1979) · Zbl 0425.13009
[3] Avramov, L.: Free Lie subalgebras of the cohomology of local rings Preprint Inst. Math. Academy of Science PO Box 373, 1090 Sofia. (To appear in Trans. of A.M.S.)
[4] Babenko, I.K.: On analytic properties of the Poincaré series of loop spaces. Math. Zametki27, 751-765 (1980); English transl. in Math. notes Vol. 27 (1980)
[5] Babenko, I.K.: On real homotopy properties of complete intersections. Math. U.S.S.R. Isvestijr, vol. 15, no2 (1980) · Zbl 0443.14012
[6] Baues, H., Lemaire, J.M.: Minimal models in homotopy theory. Math. An.225, 219-242 (1977) · Zbl 0332.55013
[7] Deligne, P., Griffiths, P., Morgan, J., sullivan, D.: The real homotopy of Kähler manifolds. Invent. Math.29, 245-274 (1975) · Zbl 0312.55011
[8] Dienes, P.: The Taylor series. New York: Dover public 1957 · Zbl 0078.05901
[9] Felix, Y., Halperin, S.: Formal space with finite dimensional rational homotopy ? preprint (1979), (to appear in Trans. of the A.M.S.)
[10] Felix, Y., Halperin, S.: Rational L.S. category and its applications ? preprint (1980). To appear in Trans. of the A.M.S.)
[11] Felix, Y., Tanré, D.: Sur la formalité des applications. Preprint (1980)
[12] Greub, V., Halperin, S., Vanstone, R.: Connections, curvature, and cohomology, III. New York: Academic press 1975
[13] Halperin, S.: Lectures on minimal models, mimeographed notes. Université de Lille I, 1977
[14] Halperin, S., Stasheff, J.D.: Obstructions to homotopy equivalences. Adv. in Math.,32, 233-279 (1979) · Zbl 0408.55009
[15] Lemaire, J.M.: Algèbres connexes et homologie des espaces de lacets. Lecture notes in Math. vol. 422. Berlin-Heidelberg-New York: Springer 1974 · Zbl 0293.55004
[16] Lemaire, J.M.: Anneaux locaux et espaces de lacets à séries de Poincaré irrationnelle. Séminaire N. Bourbaki 80/81. Exposé no 570
[17] Koszul, J.L.: Homologie et cohomologie des algèbres de Lie. Bull. Soc. Math. de France78, 65-127 (1950) · Zbl 0039.02901
[18] Miller, T.J.: On the formality of (k?1) connected compact manifolds of dimension less than or equal to 4k?2. Ill. J. of Math.23, 253-258 (1979) · Zbl 0412.57014
[19] Milnor, J., Moore, J.C.: On the structure of Hopf algebras. Ann. of Math. (2)81, 211-264 (1965) · Zbl 0163.28202
[20] Neisendorfer, J.: Formal and coformal spaces. Notre Dame Preprint · Zbl 0396.55011
[21] Neisendorfer, J.: The rational homotopy groups of complete intersections. Notre Dame Preprint · Zbl 0412.55006
[22] Oukili, A.: Sur l’homologie d’une algèbre différentielle (de Lie). Thèse (3ème cycle), Université de Nice, 1978
[23] Sullivan, D.: Infinitesimal computations in topology. Inst. Hautes Etudes Sci. publ. math.47, 269-331 (1978) · Zbl 0374.57002
[24] Thomas, J.C.: Notes aux C.R.A.S. Paris. tome290, 811-814 et 1017-1020 (1980)
[25] Thomas, J.C.: Eilenberg-Moore models for fibrations (to appear in Trans. of A.M.S.)
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