Geodesic
Smooth Actions of $p$-Toral Groups on $\mathbb Z$-Acyclic Manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 283-290.

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For a $p$-toral group $G$, we answer the question which compact (respectively, open) smooth manifolds $M$ can be diffeomorphic to the fixed point sets of smooth actions of $G$ on compact (respectively, open) smooth manifolds $E$ of the homotopy type of a finite $\mathbb Z$-acyclic CW complex admitting a cellular map of period $p$, with exactly one fixed point. In the case where the CW complex is contractible, $E$ can be chosen to be a disk (respectively, Euclidean space). 
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     author = {Krzysztof M. Pawa{\l}owski and Jan Pulikowski},
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Krzysztof M. Pawałowski; Jan Pulikowski. Smooth Actions of $p$-Toral Groups on $\mathbb Z$-Acyclic Manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 283-290. http://geodesic.mathdoc.fr/item/TM_2019_305_a14/

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