$\textbf {Z}/p\textbf {Z}$ actions on $(S^ n)^ k$
HTML articles powered by AMS MathViewer
- by Alejandro Adem PDF
- Trans. Amer. Math. Soc. 300 (1987), 791-809 Request permission
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
- Glen E. Bredon, Introduction to compact transformation groups, Pure and Applied Mathematics, Vol. 46, Academic Press, New York-London, 1972. MR 0413144
- Glen E. Bredon, Cohomological aspects of transformation groups, Proc. Conf. on Transformation Groups (New Orleans, La., 1967) Springer, New York, 1968, pp.Β 245β280. MR 0244990
- William Browder, Cohomology and group actions, Invent. Math. 71 (1983), no.Β 3, 599β607. MR 695909, DOI 10.1007/BF02095996
- Kenneth S. Brown, Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York, 1994. Corrected reprint of the 1982 original. MR 1324339
- Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0144979
- Gunnar Carlsson, On the rank of abelian groups acting freely on $(S^{n})^{k}$, Invent. Math. 69 (1982), no.Β 3, 393β400. MR 679764, DOI 10.1007/BF01389361
- N. E. Steenrod, Cohomology operations, Annals of Mathematics Studies, No. 50, Princeton University Press, Princeton, N.J., 1962. Lectures by N. E. Steenrod written and revised by D. B. A. Epstein. MR 0145525
- Richard G. Swan, $K$-theory of finite groups and orders, Lecture Notes in Mathematics, Vol. 149, Springer-Verlag, Berlin-New York, 1970. MR 0308195
- C. T. C. Wall, Finiteness conditions for $\textrm {CW}$-complexes, Ann. of Math. (2) 81 (1965), 56β69. MR 171284, DOI 10.2307/1970382
Additional Information
- © Copyright 1987 American Mathematical Society
- 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