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)

 
 

 

$ {\bf Z}/p{\bf Z}$ actions on $ (S\sp n)\sp k$


Author: Alejandro Adem
Journal: Trans. Amer. Math. Soc. 300 (1987), 791-809
MSC: Primary 57S17; Secondary 55R91, 57S25
DOI: https://doi.org/10.1090/S0002-9947-1987-0876479-6
MathSciNet review: 876479
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {\mathbf{Z}}/p$ act on a finitistic space $ X$ with integral cohomology isomorphic to that of $ {({S^n})^k}$ as a ring. We show a direct relationship between the $ {\mathbf{Z}}/p$-module structure of $ {H^n}(X;{\mathbf{Z}})$ and the nature of the fixed-point set. In particular, we obtain a significant restriction on $ {H^n}(X;{\mathbf{Z}})$ for free actions.


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

  • [Bre1] G. Bredon, Introduction to compact transformation groups, Academic Press, 1972. MR 0413144 (54:1265)
  • [Bre2] -, Cohomological aspects of transformation groups, Proc. Conf. Transformation Groups (New Orleans, 1967), Springer, 1968, pp. 245-280. MR 0244990 (39:6303)
  • [Bro] W. Browder, Cohomology and group actions, Invent. Math. 71 (1983). MR 695909 (85m:57022a)
  • [Brown] K. S. Brown, Cohomology of groups, Graduate Texts in Math., no. 87, Springer-Verlag, 1984. MR 1324339 (96a:20072)
  • [C-R] C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, Interscience, New York, 1962. MR 0144979 (26:2519)
  • [Ca] G. Carlsson, On the rank of abelian groups acting freely on $ {({S^n})^k}$, Invent. Math. 69 (1982). MR 679764 (84e:57033)
  • [S-E] N. Steenrod and D. Epstein, Cohomology operations, Ann. of Math. Studies, no. 50, Princeton Univ. Press., Princeton, N. J., 1962. MR 0145525 (26:3056)
  • [Sw] R. Swan, $ K$-theory of finite groups and orders, Lecture Notes in Math., vol. 149, Springer-Verlag, 1970. MR 0308195 (46:7310)
  • [W] C. T. C. Wall, Finiteness conditions for CW-complexes, Ann. of Math. 81 (1965), 59-69. MR 0171284 (30:1515)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57S17, 55R91, 57S25

Retrieve articles in all journals with MSC: 57S17, 55R91, 57S25


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1987-0876479-6
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society