Elementary abelian $2$-groups that act freely on products of real projective spaces
HTML articles powered by AMS MathViewer
- by Larry W. Cusick PDF
- Proc. Amer. Math. Soc. 87 (1983), 728-730 Request permission
Abstract:
For a natural number $N$ let $\bar N$ be 0 if $N$ is even and 1 if $N$ is odd. We prove that if ${({Z_2})^l}$ acts freely on $\prod _l^k{ = 1}{\mathbf {R}}{P^{{N_l}}}$ in such a way that the induced action on $\mod 2$ cohomology is trivial, then $l \leqslant 2({\bar N_1} + \cdots + {N_k})$. If no ${N_l}$ is congruent to $3\mod 4$ then $l \leqslant {\bar N_1} + \cdots + {\bar N_k}$.References
- Gunnar Carlsson, On the nonexistence of free actions of elementary abelian groups on products of spheres, Amer. J. Math. 102 (1980), no. 6, 1147–1157. MR 595008, DOI 10.2307/2374182 —, On the rank of abelian groups acting freely on ${({S^n})^k}$. Invent. Math. (to appear).
- Marvin J. Greenberg, Lectures on forms in many variables, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0241358
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 728-730
- MSC: Primary 57S17; Secondary 57S25
- DOI: https://doi.org/10.1090/S0002-9939-1983-0687651-4
- MathSciNet review: 687651