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Transactions of the American Mathematical Society

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Homotopy theory of minimal simplicial spaces

Author: Mark D. Pritt
Journal: Trans. Amer. Math. Soc. 322 (1990), 95-119
MSC: Primary 55U10
MathSciNet review: 1010889
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Abstract: Various aspects of homotopy theory in the category of minimal simplicial spaces are studied. It is shown that the usual results of homotopy theory hold in this category, and necessary and sufficient conditions are given under which a simplicial space has the homotopy type of a minimal simplicial space. Continuous cohomology in this category is also studied.

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  • [1] R. Arens, Topologies for homeomorphism groups, Amer. J. Math. 68 (1946), 593-610. MR 0019916 (8:479i)
  • [2] A. Borel and N. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Princeton Univ. Press, Princeton, N.J., 1980. MR 554917 (83c:22018)
  • [3] E. H. Brown and R. H. Szczarba, Continuous cohomology and real homotopy type, Trans. Amer. Math. Soc. 311 (1989), 57-106. MR 929667 (89f:55005)
  • [4] E. Curtis, Simplicial homotopy theory, mimeographed lecture notes, Aarhus Universitet.
  • [5] A. Haefliger, Feuilletages sur les variétés ouvertes, Topology 9 (1970), 183-194. MR 0263104 (41:7709)
  • [6] J. P. May, Simplicial objects in algebraic topology, Univ. of Chicago Press, Chicago, Ill., 1982. MR 1206474 (93m:55025)
  • [7] G. Segal, Classifying spaces and spectral sequences, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 105-112. MR 0232393 (38:718)
  • [8] -, Classifying spaces related to foliations, Topology 17 (1978), 367-382. MR 516216 (80h:57036)
  • [9] N. E. Steenrod, A convenient category of topological spaces, Michigan Math. J. 14 (1967), 133-152. MR 0210075 (35:970)
  • [10] W. T. Van Est, On the algebraic cohomology concepts in Lie groups. I, II, Nederl. Akad. Wetensch. Proc. Ser. A 58 (1955), 225-233, 286-294. MR 0070959 (17:61b)

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Keywords: Simplicial space, minimal, continuous cohomology
Article copyright: © Copyright 1990 American Mathematical Society

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