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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Homology and cohomology of $\Pi$-algebras

Authors: W. G. Dwyer and D. M. Kan
Journal: Trans. Amer. Math. Soc. 342 (1994), 257-273
MSC: Primary 55Q99; Secondary 55S99, 55U99
MathSciNet review: 1147399
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Abstract: We study a type of homological algebra associated to the collection of all homotopy groups of a space (just as the theory of group homology is associated to the fundamental group).

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  • A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR 0365573
  • W. G. Dwyer and D. M. Kan, Normalizing the cyclic modules of Connes, Comment. Math. Helv. 60 (1985), no. 4, 582–600. MR 826872, DOI
  • ---, The enveloping ring of a $\Pi$-algebra, Advances in Homotopy Theory, London Math. Soc. Lecture Note Ser., vol. 139, Cambridge Univ. Press, Cambridge, 1989, pp. 49-60.
  • Daniel M. Kan, On the homotopy relation for c.s.s. maps, Bol. Soc. Mat. Mexicana 2 (1957), 75–81. MR 0096210
  • Saunders Mac Lane, Homology, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Reprint of the 1975 edition. MR 1344215
  • J. W. Milnor, On the construction FK, London Math. Soc. Lecture Note Ser., vol. 4, Cambridge Univ. Press, Cambridge, 1972, pp. 119-136.
  • Daniel G. Quillen, Homotopical algebra, Lecture Notes in Mathematics, No. 43, Springer-Verlag, Berlin-New York, 1967. MR 0223432
  • Daniel Quillen, On the (co-) homology of commutative rings, Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVII, New York, 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 65–87. MR 0257068
  • Christopher R. Stover, A van Kampen spectral sequence for higher homotopy groups, Topology 29 (1990), no. 1, 9–26. MR 1046622, DOI
  • George W. Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics, vol. 61, Springer-Verlag, New York-Berlin, 1978. MR 516508

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Article copyright: © Copyright 1994 American Mathematical Society