Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The Postnikov Tower and the Steenrod problem


Author: Ming-Li Chen
Journal: Proc. Amer. Math. Soc. 129 (2001), 1825-1831
MSC (1991): Primary 55R91, 55S45, 55S91
DOI: https://doi.org/10.1090/S0002-9939-00-05766-X
Published electronically: October 31, 2000
MathSciNet review: 1814116
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The Steenrod problem asks: given a $G$-module, when does there exist a Moore space realizing the module? By using the equivariant Postnikov Tower, it is shown that a $\mathbb{Z} G$-module is $\mathbb{Z} G$-realizable if and only if it is $\mathbb{Z} H$-realizable for all $p$-Sylow subgroups $H$, for all primes $p\vert\vert G\vert$.


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

  • 1. J. Arnold, A Solution of a Problem of Steenrod for Cyclic Groups of Prime Order, Proc. Amer. Math. Soc. 62 (1977), 177-182. MR 55:4152
  • 2. J. Arnold, On Steenrod's Problem for Cyclic $p$-Groups, Canad. J. Math. 29 (1977), 421-428. MR 55:13411
  • 3. A. Assadi, Homotopy Actions and Cohomology of Finite Groups, Transformation Groups, Poznan 1985, Springer, LNM 1217. MR 88d:55005
  • 4. D. Benson and N. Habegger, Varieties for Modules and a Problem of Steenrod, J. Pure and Applied Algebra, 44 (1987), 13-34. MR 88e:55020
  • 5. G. Bredon, Equivariant Cohomology Theories, LNM 34, 1967. MR 35:4914
  • 6. G. Bredon, Equivariant Cohomology Theories, Bull. AMS 73 (1967), 266-268. MR 34:6762
  • 7. K. Brown, Cohomology of Groups, Springer-Verlag, 1982. MR 83k:20002
  • 8. G. Carlsson, A Counterexample to a Conjecture of Steenrod, Invent. Math. 64 (1981) 171-174. MR 82j:57036
  • 9. G. Cooke, Replacing Homotopy Actions by Topological Actions, Trans. AMS 237 (1978), 391-406. MR 57:1529
  • 10. A. Dold and R. Lashof, Principal Qusi-fibrations and Fibre Homotopy Equivalence of Bundles, Illinois J. Math. 3 (1959), 285-305. MR 21:331
  • 11. S. Eilenberg, Homology of Spaces with Operators I, Trans. AMS 61 (1947), 378-417; errata, 62 (1947), 548. MR 9:52b
  • 12. P. Kahn, Steenrod Problem and $k$-invariants of Certain Classifying Spaces, Algebraic K-Theory, Proc. Oberwolfach 1980, Part 2, LNM, 967. MR 84k:57030
  • 13. R. Lashof, Problems in Differential and Algebraic Topology, Seattle Topology Conference, Ann. Math. (1965). MR 32:443
  • 14. R. Mosher and M. Tangora, Cohomology Operations and Applications in Homotopy Theory, Harper & Row, 1968. MR 37:2223
  • 15. J. Stasheff, A Classification Theorem for Fibre Spaces, Topology 2 (1963), 239-246. MR 27:4235
  • 16. R. Swan, Invariant Rational Functions and A Problem of Steenrod, Invent. Math. 7 (1969), 148-158. MR 39:5532
  • 17. P. Vogel, On Steenrod Problem for Non-abelian Finite Groups, Proc. Alg. Top. Conf. Aarhus 1982, Springer LNM 1051 (1984). MR 86e:55015
  • 18. P. Vogel, A Solution of the Steenrod Problem for G-Moore Spaces, K-Theory 1 (1987), 325-335. MR 89e:57033
  • 19. G.W. Whitehead, Elements of Homotopy Theory, Springer-Verlag, 1978. MR 80b:55001

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 55R91, 55S45, 55S91

Retrieve articles in all journals with MSC (1991): 55R91, 55S45, 55S91


Additional Information

Ming-Li Chen
Affiliation: Center for the Mathematical Sciences, University of Wisconsin, Madison, Wisconsin 53715
Email: mchen@cms.wisc.edu

DOI: https://doi.org/10.1090/S0002-9939-00-05766-X
Received by editor(s): June 18, 1997
Received by editor(s) in revised form: September 13, 1999
Published electronically: October 31, 2000
Communicated by: Ralph Cohen
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society