Equivariant algebraic topology

Sören Illman

Annales de l'institut Fourier (1973)

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

Abstract

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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 C W -complexes and mention some of their basic properties.The paper is a short abstract and contains no proofs.

How to cite

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Illman, 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

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  1. [1] G. BREDON, Equivariant cohomology theories, Bull. Amer. Math. Soc., 73 (1967), 269-273. Zbl0162.27301
  2. [2] G. BREDON, Equivariant cohomology theories, Lecture Notes in Mathematics, Vol. 34, Springer-Verlag (1967). Zbl0162.27202MR35 #4914
  3. [3] T. BRÖCKER, Singuläre Definition der Äquivarianten Bredon Homologie, Manuscripta Matematica 5 (1971), 91-102. Zbl0213.49902
  4. [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. [5] S. ILLMAN, Equivariant Algebraic Topology, Thesis, Princeton University (1972). 
  6. [6] S. ILLMAN, Equivariant singular homology and cohomology. To appear in Bull. Amer. Math. Soc. Zbl0297.55003
  7. [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. [8] R. PALAIS, The classification of G-spaces, Memoirs of Amer. Math. Soc., 36 (1960). Zbl0119.38403MR31 #1664
  9. [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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