On extending free group actions on spheres and a conjecture of Iwasawa

Connolly, Frank; Geist, Robert

doi:10.1090/S0002-9947-1982-0675071-1

On extending free group actions on spheres and a conjecture of Iwasawa
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by Frank Connolly and Robert Geist

Trans. Amer. Math. Soc. 274 (1982), 631-640

DOI: https://doi.org/10.1090/S0002-9947-1982-0675071-1

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Abstract:

A transfer map for Reidemeister torsion is defined and used to determine whether free actions of $\mathbf {Z}/k$ on $S^{2n+1}$, $n > 1$, extend to free actions of $\mathbf {Z}/hk$. It is shown that for $k$ odd, every free $\mathbf {Z}/k$ action on $S^{2n+1}$, $n > 1$, extends to a free $\mathbf {Z}/2k$ action. For prime $p$, extension of an arbitrary free $\mathbf {Z}/p$ action to a free $\mathbf {Z}/p^{2}$ action is reduced to a long-standing conjecture of Iwasawa.

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