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Obstructions to homotopy equivalences. (English) Zbl 0408.55009


MSC:

55P62 Rational homotopy theory
55P10 Homotopy equivalences in algebraic topology
55T20 Eilenberg-Moore spectral sequences
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[1] Adams, J. F., On the cobar construction, (Proc. Nat. Acad. Sci. USA, 42 (1956)), 409-412 · Zbl 0071.16404
[2] Baues, H. J., Rationale homotopietypen, ((1975)), 1-13, Bonn preprint · Zbl 0354.55003
[3] Baues, H. J.; Lemaire, J. M., Minimal models in homotopy theory, Math. Ann., 225, 219-242 (1977) · Zbl 0322.55019
[4] Body, R. A.; Douglas, R. R., Homotopy types within a rational homotopy type, Topology, 13, 209-214 (1974) · Zbl 0299.55008
[5] Bousfield, A. K.; Gugenheim, V. K.A. M., On PL DeRham theory and rational homotopy type, Mem. Amer. Math. Soc., 179 (1976) · Zbl 0338.55008
[6] Bousfield, A. K.; Kan, D. M., The homotopy spectral sequence of a space with coefficients in a ring, Topology, 11, 29-106 (1972) · Zbl 0202.22803
[7] Bousfield, A. K.; Kan, D. M., Homotopy Limits, Completions, and Localization, (Lecture Notes in Mathematics No. 304 (1972), Springer-Verlag: Springer-Verlag Berlin/New York) · Zbl 0259.55004
[8] Cartan, H., La transgression dans un groupe de Lie et dans un espace fibré principal, (Colloque de Topologie (espaces fibrés) Bruxelles 1950 (1951), Masson et Cie: Masson et Cie Liege et Paris), 15-27 · Zbl 0045.30701
[9] Cartan, H., Notion de Construction, Séminaire H. Cartan, École Norm. Sup. Paris, Exposé, 3 (1954-1955)
[10] Deliqne, P.; Griffiths, P.; Morgan, J.; Sullivan, D., The real homotopy theory of Kähler manifolds, Invent. Math., 29, 245-254 (1975) · Zbl 0312.55011
[11] Eilenberg, S.; MacLane, S., On the groups H (π, n) I, Ann. of Math., 58, 55-106 (1953) · Zbl 0050.39304
[12] Eilenberg, S.; Moore, J. C., Homology and fibrations I, Comment. Math. Helv., 40, 199-236 (1966) · Zbl 0148.43203
[13] Greub, W. H.; Halperin, S.; Vanstone, J. R., (Connections, Curvature, and Cohomology, Vol. III (1976), Academic Press: Academic Press New York) · Zbl 0372.57001
[14] Gugenheim, V. K.A. M.; May, J. P., On the theory and applications of differential torsion products, Mem. Amer. Math. Soc., 142 (1974) · Zbl 0292.55019
[15] Gugenheim, V. K.A. M.; Milgram, R. J., On successive approximations in homological algebra, Trans. Amer. Math. Soc., 150, 157-182 (1970) · Zbl 0233.55012
[16] S. Halperin; S. Halperin · Zbl 0536.55003
[17] Hilton, P. J., On the homotopy groups of a union of spheres, J. London Math. Soc., 30, 154-171 (1955) · Zbl 0064.17301
[18] Koszul, J.-L, Sur un type d’algebres differentielles en rapport avec la transgression, (Colloque de Topologie (espaces fibrés) Bruxelles 1950 (1951), Masson et Cie: Masson et Cie Liege et Paris), 73-81 · Zbl 0045.30801
[19] MacLane, S., Homology (1967), Springer-Verlag: Springer-Verlag Berlin/New York · Zbl 0133.26502
[20] May, J. P., Matric Massey products, J. Algebra, 12, 533-568 (1969) · Zbl 0192.34302
[21] May, J. P., Simplicial Objects in Algebraic Topology (1967), Van Nostrand: Van Nostrand Princeton, N.J · Zbl 0165.26004
[22] Mimura, M.; Nishida, G.; Toda, H., Localization of CW complexes and applications, J. Math. Soc. Japan, 23, 593-624 (1971) · Zbl 0217.48801
[23] Moore, J. C., Some properties of the loop homology of commutative coalgebras, (The Steenrod Algebra and its Applications. The Steenrod Algebra and its Applications, LNM, 168 (1970)), 235-245 · Zbl 0211.55101
[24] Moore, J. C., Further properties of the loop homology of commutative coalgebras, (Proc. Advan. Study Inst. Alg. Top. (1970)), 393-411, Aarhus · Zbl 0233.16012
[25] Neisendorfer, J.; Miller, T., Formal and coformal spaces, Illinois J. Math., 22, 565-580 (1978) · Zbl 0396.55011
[26] Onishchik, A. L., Topological invariants of homogeneous spaces, Mat. Zametki, 12, No. 6, 761-768 (1972) · Zbl 0246.57018
[27] Quillen, D., Rational homotopy theory, Ann. of Math., 90, 205-295 (1969) · Zbl 0191.53702
[28] Smith, L., The Eilenberg-Moore spectral sequence, Trans. Amer. Math. Soc., 129, 58-93 (1967) · Zbl 0177.51402
[29] Sullivan, D., Geometric topology. I. Localization, periodicity, and Galois summetry, duplicated notes (1970), M.I.T
[30] D. Sullivan; D. Sullivan
[31] Tate, J., Homology of noetherian rings and local rings, Illinois J. Math., 1, 14-27 (1957) · Zbl 0079.05501
[32] Thom, R., Operations en cohomologie réelle, Séminaire H. Cartan, École Norm. Sup., Exposé, 17 (1954-1955)
[33] Toomer, G. H., Two applications of homology decompositions, Canad. J. Math., 27, 323-329 (1975) · Zbl 0299.55010
[34] Curtis, E. B., Some relations between homotopy and homology, Ann. of Math., 83, 386-413 (1965) · Zbl 0139.16503
[35] Jozefiak, J. T., Tate resolutions for commutative graded algebras over a local ring, Fund. Math., 74, 209-231 (1972) · Zbl 0236.13012
[36] Lemaire, J. M., Algebras Connexes et Homologie des Espaces de Lacets, (Lecture Notes in Mathematics No. 422 (1974), Springer-Verlag: Springer-Verlag Berlin/New York) · Zbl 0293.55004
[37] Quillen, D., On the (co)-homology of commutative rings, (Amer. Math. Soc. Symp. in Pure Math., 17 (1970)), 65-87 · Zbl 0234.18010
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