Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Equivariant homology theories on $ G$-complexes


Author: Stephen J. Willson
Journal: Trans. Amer. Math. Soc. 212 (1975), 155-171
MSC: Primary 55B25
DOI: https://doi.org/10.1090/S0002-9947-1975-0377859-X
MathSciNet review: 0377859
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A definition is given for a ``cellular'' equivariant homology theory on G-complexes. The definition is shown to generalize to G-complexes with prescribed isotropy subgroups. A ring I is introduced to deal with the general definition. One obtains a universal coefficient theorem and studies the universal coefficients.


References [Enhancements On Off] (What's this?)

  • [1] G. E. Bredon, Equivariant cohomology theories, Bull. Amer. Math. Soc. 73 (1967), 266-268. MR 34 #6762. MR 0206946 (34:6762)
  • [2] -, Equivariant cohomology theories, Lecture Notes in Math., no. 34, Springer-Verlag, Berlin and New York, 1967. MR 35 #4914. MR 0214062 (35:4914)
  • [3] Th. Bröcker, Singuläre Definition der äquivarianter Bredon Homologie, Manuscripta Math. 5 (1971), 91-102. MR 45 #2695. MR 0293618 (45:2695)
  • [4] Eldon Dyer, Cohomology theories, Math. Lecture Notes Series, Benjamin, New York, 1969. MR 42 #3780. MR 0268883 (42:3780)
  • [5] Sören Illman, Equivariant algebraic topology, Thesis, Princeton University, Princeton, N. J., 1972.
  • [6] -, Equivariant singular homology and cohomology for actions of compact Lie groups, Proc. Conf. on Transformation Groups, Lecture Notes in Math., no. 298, Springer-Verlag, Berlin and New York, 1972. MR 0377858 (51:14027)
  • [7] -, Equivariant singular homology and cohomology, Bull. Amer. Math. Soc. 79 (1973), 188-192. MR 46 #6340. MR 0307220 (46:6340)
  • [8] C. N. Lee, Equivariant homology theories, Proc. Conf. on Transformation Groups (New Orleans, La., 1967), Springer, New York, 1968, pp. 237-244. MR 40 #3538. MR 0250299 (40:3538)
  • [9] Saunders Mac Lane, Homology, Die Grundlehren der math. Wissenschaften, Band 114, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #122.
  • [10] T. Matumoto, Equivariant K-theory and Fredholm operators, J. Fac. Sci. Univ. Tokyo Sect IA Math. 18 (1971), 109-125. MR 44 #7538. MR 0290354 (44:7538)
  • [11] C. Vaseekaran, Equivariant homotopy theory, Bull. Amer. Math. Soc. 80 (1974), 322-324. MR 0331389 (48:9722)
  • [12] S. J. Willson, Equivariant homology theories, Thesis, University of Michigan, Ann Arbor, Mich., 1973.
  • [13] -, Equivariant maps between representation spheres, Pacific J. Math. 56 (1975). MR 0394715 (52:15514)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 55B25

Retrieve articles in all journals with MSC: 55B25


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0377859-X
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society