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

Zbigniew Fiedorowicz; Wojciech Gajda

Fundamenta Mathematicae (1994)

- Volume: 145, Issue: 1, page 91-100
- ISSN: 0016-2736

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topFiedorowicz, Zbigniew, and Gajda, Wojciech. "The S1-CW decomposition of the geometric realization of a cyclic set." Fundamenta Mathematicae 145.1 (1994): 91-100. <http://eudml.org/doc/212036>.

@article{Fiedorowicz1994,

abstract = {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.},

author = {Fiedorowicz, Zbigniew, Gajda, Wojciech},

journal = {Fundamenta Mathematicae},

keywords = {cyclic set; $S^1-CW$ complex; equivariant homology theory; geometric realization of a cyclic set; -equivariant, cellular decomposition; cyclic homology of a cyclic space; -equivariant Borel homology},

language = {eng},

number = {1},

pages = {91-100},

title = {The S1-CW decomposition of the geometric realization of a cyclic set},

url = {http://eudml.org/doc/212036},

volume = {145},

year = {1994},

}

TY - JOUR

AU - Fiedorowicz, Zbigniew

AU - Gajda, Wojciech

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

JO - Fundamenta Mathematicae

PY - 1994

VL - 145

IS - 1

SP - 91

EP - 100

AB - 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.

LA - eng

KW - cyclic set; $S^1-CW$ complex; equivariant homology theory; geometric realization of a cyclic set; -equivariant, cellular decomposition; cyclic homology of a cyclic space; -equivariant Borel homology

UR - http://eudml.org/doc/212036

ER -

## References

top- [1] M. Bökstedt, W. C. Hsiang and I. Madsen, The cyclotomic trace and algebraic K-theory of spaces, Invent. Math. 111 (1993), 465-539. Zbl0804.55004
- [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. Zbl0639.55003
- [4] A. Connes, Cohomologie cyclique et foncteurs $Ex{t}^{n}$, 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. Zbl0702.55014
- [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. Zbl0755.18005
- [9] T. Goodwillie, Cyclic homology, derivations, and the free loopspace, Topology 24 (1985), 187-215. Zbl0569.16021
- [10] T. Kawasaki, Cohomology of twisted projective spaces and lens complexes, Math. Ann. 206 (1973), 243-248. Zbl0268.57005
- [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. Zbl0477.55009
- [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. Zbl0199.26404
- [16] G. Segal, Categories and cohomology theories, Topology 13 (1974), 293-314. Zbl0284.55016
- [17] J. Słomińska, Equivariant singular cohomology of unitary representation spheres for finite groups, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), 627-632. Zbl0503.55004
- [18] S. J. Willson, Equivariant homology theories on G-complexes, Trans. Amer. Math. Soc. 212 (1975), 155-171. Zbl0308.55002

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