|
Systems of fixed point sets
Author:
A. D. Elmendorf
Journal:
Trans. Amer. Math. Soc. 277 (1983), 275-284
MSC:
Primary 57S99; Secondary 55N25
MathSciNet review:
690052
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: Let  be a compact Lie group. A canonical method is given for constructing a  -space from homotopy theoretic information about its fixed point sets. The construction is a special case of the categorical bar construction. Applications include easy constructions of certain classifying spaces, as well as  -Eilenberg-Mac Lane spaces and Postnikov towers.
- [1]
Glen
E. Bredon, Equivariant cohomology theories, Lecture Notes in
Mathematics, No. 34, Springer-Verlag, Berlin, 1967. MR 0214062
(35 #4914)
- [2]
Tammo
tom Dieck, Transformation groups and representation theory,
Lecture Notes in Mathematics, vol. 766, Springer, Berlin, 1979. MR 551743
(82c:57025)
- [3]
Sören
Illman, Equivariant singular homology and cohomology. I, Mem.
Amer. Math. Soc. 1 (1975), no. issue 2, 156, ii+74.
MR
0375286 (51 #11482)
- [4]
J. McClure, Some remarks on Elmendorf's construction (preprint).
- [5]
J.
Peter May, Classifying spaces and fibrations, Mem. Amer. Math.
Soc. 1 (1975), no. 1, 155, xiii+98. MR 0370579
(51 #6806)
- [6]
Georgia
Višnjić Triantafillou, Äquivariante rationale
Homotopietheorie, Bonner Mathematische Schriften [Bonn Mathematical
Publications], 110, Universität Bonn Mathematisches Institut, Bonn,
1978 (German). Dissertation, Rheinische Friedrich-Wilhelms-Universität
Bonn, Bonn, 1977. MR 552277
(81a:55021)
- [7]
Stefan
Waner, Equivariant classifying spaces and
fibrations, Trans. Amer. Math. Soc.
258 (1980), no. 2,
385–405. MR
558180 (82m:55016c), http://dx.doi.org/10.1090/S0002-9947-1980-0558180-5
- [1]
- G. E. Bredon, Equivariant cohomology theories, Lecture Notes in Math., vol. 34, Springer-Verlag, Berlin and New York, 1967. MR 0214062 (35:4914)
- [2]
- T. tom Dieck, Transformation groups and representation theory, Lecture Notes in Math., vol. 766, Springer-Verlag, Berlin and New York, 1979. MR 551743 (82c:57025)
- [3]
- S. Illman, Equivariant singular homology and cohomology, I, Mem. Amer. Math. Soc. No. 156 (1975). MR 0375286 (51:11482)
- [4]
- J. McClure, Some remarks on Elmendorf's construction (preprint).
- [5]
- J. P. May, Classifying spaces andfibrations, Mem. Amer. Math. Soc. No. 155 (1975). MR 0370579 (51:6806)
- [6]
- G. Triantafillou, Äquivariante rationale homotopietheorie, Bonner Math. Schriften 110, Bonn, 1978. MR 552277 (81a:55021)
- [7]
- S. Waner, Equivariant homotopy and Milnor's theorem, Trans. Amer. Math. Soc. 258 (1980), 385-405. MR 558180 (82m:55016c)
Similar Articles
Retrieve articles in Transactions of the American Mathematical Society
with MSC:
57S99,
55N25
Retrieve articles in all journals
with MSC:
57S99,
55N25
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1983-0690052-0
PII:
S 0002-9947(1983)0690052-0
Keywords:
Equivariant homotopy
Article copyright:
© Copyright 1983 American Mathematical Society
|
