Applications of perturbation theory to iterated fibrations

For a class of spaces including simply connected spaces and classifying spaces of nilpotent groups, relatively small differential graded algebras are constructed over commutative rings with 1 which are chain homotopy equivalent to the singular cochain algebra. An application to finitely generated torsion-free nilpotent groups over the integers is given.

[1]  W. Cockcroft.  The cohomology groups of a fibre space with fibre a space of type (,). II , 1959 .

[2]  Dennis Sullivan,et al.  Infinitesimal computations in topology , 1977 .

[3]  R. H. Szczarba,et al.  THE HOMOLOGY OF TWISTED CARTESIAN PRODUCTS , 1961 .

[4]  Jon P. May,et al.  On the theory and applications of differential torsion products , 1974 .

[5]  J. C. Moore,et al.  On Semisimplicial Fibre-Bundles , 1959 .

[6]  Saunders MacLane,et al.  On the Groups H(Π, n), II: Methods of Computation , 1954 .

[7]  V. K. A. M. Gugenheim,et al.  On the chain-complex of a fibration , 1972 .

[8]  D. Quillen,et al.  Rational homotopy theory , 1969 .

[9]  Charles Terence Clegg Wall,et al.  Resolutions for extensions of groups , 1961, Mathematical Proceedings of the Cambridge Philosophical Society.

[10]  V. Gugenheim,et al.  On the extended functoriality of Tor and Cotor , 1974 .

[11]  Kochendörffer.  S. MacLane, Homology (Die Grundlehren der mathematischen Wissenschaften, Band 114). X + 422 S. mit 7 Fig. Berlin/Göttingen/Heidelberg 1963. Springer-Verlag. Preis geb. DM 62,– , 1963 .

[12]  Cohomology of nilmanifolds and torsion-free, nilpotent groups , 1982 .

[13]  Samuel Eilenberg,et al.  On the Groups H(Π, n), I , 1953 .

[14]  Jim Stasheff,et al.  Homotopy associativity of $H$-spaces. II , 1963 .

[15]  P. Hilton.  Homotopy Theory and Duality , 1965 .

[16]  Jon P. May.  Simplicial objects in algebraic topology , 1993 .

[17]  A. Wasserman,et al.  On the groups () , 1975 .

[18]  V. Gugenheim.  On a theorem of E. H. Brown , 1960 .

[19]  W. Cockcroft.  ON A THEOREM OF A. BOREL , 1961 .

[20]  John C. Moore,et al.  Differential homological algebra and homogeneous spaces , 1974 .

[21]  V. K. A. M. Gugenheim,et al.  On a perturbation theory for the homology of the loop-space , 1982 .

[22]  The cohomology groups of a fibre space with fibre a space of type ( , 1956 .