Orientation preserving actions of finite abelian groups on spheres
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- by Ronald M. Dotzel PDF
- Proc. Amer. Math. Soc. 100 (1987), 159-163 Request permission
Abstract:
If $G$ is a finite Abelian group acting as a ${{\mathbf {Z}}_{(\mathcal {P})}}$-homology $n$-sphere $X$ (where $\mathcal {P}$ is the set of primes dividing $|G|)$, then there is an integer valued function $n(,G)$ defined on the prime power subgroups $H$ of $G$ such that ${X^H}$ has the ${{\mathbf {Z}}_{(p)}}$-homology of a sphere ${S^{n(H,G)}}$. We prove here that there exists a real representation $R$ of $G$ such that for any prime power subgroup $H$ of $G,\dim (S({R^H})) = n(H,G)$ where $S({R^H})$ is the unit sphere of ${R^H}$, provided that $n - n(H,G)$ is even whenever $H$ is a $2$-subgroup of $G$.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 159-163
- MSC: Primary 57S17; Secondary 57S25
- DOI: https://doi.org/10.1090/S0002-9939-1987-0883421-6
- MathSciNet review: 883421