The S1-CW decomposition of the geometric realization of a cyclic set
Fiedorowicz, Zbigniew ; Gajda, Wojciech
Fundamenta Mathematicae, Tome 144 (1994), p. 91-100 / Harvested from The Polish Digital Mathematics Library

We show that the geometric realization of a cyclic set has a natural, S1-equivariant, cellular decomposition. As an application, we give another proof of a well-known isomorphism between cyclic homology of a cyclic space and S1-equivariant Borel homology of its geometric realization.

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:212036
@article{bwmeta1.element.bwnjournal-article-fmv145i1p91bwm,
     author = {Zbigniew Fiedorowicz and Wojciech Gajda},
     title = {The S1-CW decomposition of the geometric realization of a cyclic set},
     journal = {Fundamenta Mathematicae},
     volume = {144},
     year = {1994},
     pages = {91-100},
     zbl = {0831.55007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv145i1p91bwm}
}
Fiedorowicz, Zbigniew; Gajda, Wojciech. The S1-CW decomposition of the geometric realization of a cyclic set. Fundamenta Mathematicae, Tome 144 (1994) pp. 91-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv145i1p91bwm/

[00000] [1] M. Bökstedt, W. C. Hsiang and I. Madsen, The cyclotomic trace and algebraic K-theory of spaces, Invent. Math. 111 (1993), 465-539. | Zbl 0804.55004

[00001] [2] K. Brown, Cohomology of Groups, Graduate Texts in Math. 87, Springer, 1982.

[00002] [3] D. Burghelea and Z. Fiedorowicz, Cyclic homology and algebraic K-theory of spaces - II, Topology 25 (1986), 303-317. | Zbl 0639.55003

[00003] [4] A. Connes, Cohomologie cyclique et foncteurs Extn, C. R. Acad. Sci. Paris 296 (1983), 953-958.

[00004] [5] T. tom Dieck, Transformation Groups, de Gruyter, 1987.

[00005] [6] G. Dunn, Dihedral and quaternionic homology and mapping spaces, K-Theory 3 (1989), 141-161. | Zbl 0702.55014

[00006] [7] G. Dunn and Z. Fiedorowicz, A classifying space construction for cyclic spaces, Math. Ann., to appear.

[00007] [8] Z. Fiedorowicz and J.-L. Loday, Crossed simplicial groups and their associated homology, Trans. Amer. Math. Soc. 326 (1991), 57-87. | Zbl 0755.18005

[00008] [9] T. Goodwillie, Cyclic homology, derivations, and the free loopspace, Topology 24 (1985), 187-215. | Zbl 0569.16021

[00009] [10] T. Kawasaki, Cohomology of twisted projective spaces and lens complexes, Math. Ann. 206 (1973), 243-248. | Zbl 0268.57005

[00010] [11] L. G. Lewis, Jr., The RO(G)-graded equivariant ordinary cohomology of complex projective spaces with linear Zp-actions, in: Lecture Notes in Math. 1361, Springer, 1988, 53-123.

[00011] [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. | Zbl 0477.55009

[00012] [13] L. G. Lewis, Jr., J. P. May and M. Steinberger, Equivariant Stable Homotopy Theory, Lecture Notes in Math. 1213, Springer, 1986.

[00013] [14] J. P. May, The Geometry of Iterated Loop Spaces, Lecture Notes in Math. 271, Springer, 1972.

[00014] [15] G. Segal, Classifying spaces and spectral sequences, Publ. IHES 34 (1968), 105-112. | Zbl 0199.26404

[00015] [16] G. Segal, Categories and cohomology theories, Topology 13 (1974), 293-314. | Zbl 0284.55016

[00016] [17] J. Słomińska, Equivariant singular cohomology of unitary representation spheres for finite groups, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), 627-632. | Zbl 0503.55004

[00017] [18] S. J. Willson, Equivariant homology theories on G-complexes, Trans. Amer. Math. Soc. 212 (1975), 155-171. | Zbl 0308.55002