Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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).

References [Enhancements On Off] (What's this?)

  • [1] 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
  • [2] W. G. Dwyer and D. M. Kan, Normalizing the cyclic modules of Connes, Comment. Math. Helv. 60 (1985), no. 4, 582–600. MR 826872, 10.1007/BF02567433
  • [3] -, 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.
  • [4] Daniel M. Kan, On the homotopy relation for c.s.s. maps, Bol. Soc. Mat. Mexicana 2 (1957), 75–81. MR 0096210
  • [5] Saunders Mac Lane, Homology, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Reprint of the 1975 edition. MR 1344215
  • [6] J. W. Milnor, On the construction FK, London Math. Soc. Lecture Note Ser., vol. 4, Cambridge Univ. Press, Cambridge, 1972, pp. 119-136.
  • [7] Daniel G. Quillen, Homotopical algebra, Lecture Notes in Mathematics, No. 43, Springer-Verlag, Berlin-New York, 1967. MR 0223432
  • [8] 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
  • [9] Christopher R. Stover, A van Kampen spectral sequence for higher homotopy groups, Topology 29 (1990), no. 1, 9–26. MR 1046622, 10.1016/0040-9383(90)90022-C
  • [10] George W. Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics, vol. 61, Springer-Verlag, New York-Berlin, 1978. MR 516508

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 55Q99, 55S99, 55U99

Retrieve articles in all journals with MSC: 55Q99, 55S99, 55U99

Additional Information

Article copyright: © Copyright 1994 American Mathematical Society