# Equivariant algebraic topology

Annales de l'institut Fourier (1973)

- Volume: 23, Issue: 2, page 87-91
- ISSN: 0373-0956

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topIllman, Sören. "Equivariant algebraic topology." Annales de l'institut Fourier 23.2 (1973): 87-91. <http://eudml.org/doc/74132>.

@article{Illman1973,

abstract = {Let $G$ be a topological group. We give the existence of an equivariant homology and cohomology theory, defined on the category of all $G$-pairs and $G$-maps, which both satisfy all seven equivariant Eilenberg-Steenrod axioms and have a given covariant and contravariant, respectively, coefficient system as coefficients.In the case that $G$ is a compact Lie group we also define equivariant $CW$-complexes and mention some of their basic properties.The paper is a short abstract and contains no proofs.},

author = {Illman, Sören},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {2},

pages = {87-91},

publisher = {Association des Annales de l'Institut Fourier},

title = {Equivariant algebraic topology},

url = {http://eudml.org/doc/74132},

volume = {23},

year = {1973},

}

TY - JOUR

AU - Illman, Sören

TI - Equivariant algebraic topology

JO - Annales de l'institut Fourier

PY - 1973

PB - Association des Annales de l'Institut Fourier

VL - 23

IS - 2

SP - 87

EP - 91

AB - Let $G$ be a topological group. We give the existence of an equivariant homology and cohomology theory, defined on the category of all $G$-pairs and $G$-maps, which both satisfy all seven equivariant Eilenberg-Steenrod axioms and have a given covariant and contravariant, respectively, coefficient system as coefficients.In the case that $G$ is a compact Lie group we also define equivariant $CW$-complexes and mention some of their basic properties.The paper is a short abstract and contains no proofs.

LA - eng

UR - http://eudml.org/doc/74132

ER -

## References

top- [1] G. BREDON, Equivariant cohomology theories, Bull. Amer. Math. Soc., 73 (1967), 269-273. Zbl0162.27301
- [2] G. BREDON, Equivariant cohomology theories, Lecture Notes in Mathematics, Vol. 34, Springer-Verlag (1967). Zbl0162.27202MR35 #4914
- [3] T. BRÖCKER, Singuläre Definition der Äquivarianten Bredon Homologie, Manuscripta Matematica 5 (1971), 91-102. Zbl0213.49902
- [4] S. ILLMAN, Equivariant singular homology and cohomology for actions of compact Lie groups. To appear in : Proceedings of the Conference on Transformation Groups at the University of Massachusetts, Amherst, June 7-18 (1971) Springer-Verlag, Lecture Notes in Mathematics. Zbl0251.55004
- [5] S. ILLMAN, Equivariant Algebraic Topology, Thesis, Princeton University (1972).
- [6] S. ILLMAN, Equivariant singular homology and cohomology. To appear in Bull. Amer. Math. Soc. Zbl0297.55003
- [7] T. MATSUMOTO, Equivariant K-theory and Fredholm operators, Journal of the Faculty of Science, The University of Tokyo, Vol. 18 (1971), 109-125. Zbl0213.25402
- [8] R. PALAIS, The classification of G-spaces, Memoirs of Amer. Math. Soc., 36 (1960). Zbl0119.38403MR31 #1664
- [9] C. T. YANG, The triangulability of the orbit space of a differentiable transformation group, Bull. Amer. Math. Soc., 69 (1963), 405-408. Zbl0114.14502MR26 #3813

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