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1994 | 145 | 1 | 91-100
Tytuł artykułu

The S1-CW decomposition of the geometric realization of a cyclic set

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Abstrakty
EN
We show that the geometric realization of a cyclic set has a natural, $S^1$-equivariant, cellular decomposition. As an application, we give another proof of a well-known isomorphism between cyclic homology of a cyclic space and $S^1$-equivariant Borel homology of its geometric realization.
Twórcy
  • Department of Mathematics, Ohio State University, 231 W. 18th Avenue, Columbus, Ohio 43210, U.S.A.
  • Institute of Mathematics, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
Bibliografia
  • [1] M. Bökstedt, W. C. Hsiang and I. Madsen, The cyclotomic trace and algebraic K-theory of spaces, Invent. Math. 111 (1993), 465-539.
  • [2] K. Brown, Cohomology of Groups, Graduate Texts in Math. 87, Springer, 1982.
  • [3] D. Burghelea and Z. Fiedorowicz, Cyclic homology and algebraic K-theory of spaces - II, Topology 25 (1986), 303-317.
  • [4] A. Connes, Cohomologie cyclique et foncteurs $Ext^n$, C. R. Acad. Sci. Paris 296 (1983), 953-958.
  • [5] T. tom Dieck, Transformation Groups, de Gruyter, 1987.
  • [6] G. Dunn, Dihedral and quaternionic homology and mapping spaces, K-Theory 3 (1989), 141-161.
  • [7] G. Dunn and Z. Fiedorowicz, A classifying space construction for cyclic spaces, Math. Ann., to appear.
  • [8] Z. Fiedorowicz and J.-L. Loday, Crossed simplicial groups and their associated homology, Trans. Amer. Math. Soc. 326 (1991), 57-87.
  • [9] T. Goodwillie, Cyclic homology, derivations, and the free loopspace, Topology 24 (1985), 187-215.
  • [10] T. Kawasaki, Cohomology of twisted projective spaces and lens complexes, Math. Ann. 206 (1973), 243-248.
  • [11] L. G. Lewis, Jr., The RO(G)-graded equivariant ordinary cohomology of complex projective spaces with linear $Z_p$-actions, in: Lecture Notes in Math. 1361, Springer, 1988, 53-123.
  • [12] L. G. Lewis, Jr., J. P. May and J. McClure, Ordinary RO(G)-graded cohomology, Bull. Amer. Math. Soc. (N.S.) 4 (1981), 208-212.
  • [13] L. G. Lewis, Jr., J. P. May and M. Steinberger, Equivariant Stable Homotopy Theory, Lecture Notes in Math. 1213, Springer, 1986.
  • [14] J. P. May, The Geometry of Iterated Loop Spaces, Lecture Notes in Math. 271, Springer, 1972.
  • [15] G. Segal, Classifying spaces and spectral sequences, Publ. IHES 34 (1968), 105-112.
  • [16] G. Segal, Categories and cohomology theories, Topology 13 (1974), 293-314.
  • [17] J. Słomińska, Equivariant singular cohomology of unitary representation spheres for finite groups, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), 627-632.
  • [18] S. J. Willson, Equivariant homology theories on G-complexes, Trans. Amer. Math. Soc. 212 (1975), 155-171.
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Bibliografia
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bwmeta1.element.bwnjournal-article-fmv145i1p91bwm
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