Geodesic
Smooth Actions of $p$-Toral Groups on $\mathbb Z$-Acyclic Manifolds
Informatics and Automation, 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). 
@article{TRSPY_2019_305_a14,
     author = {Krzysztof M. Pawa{\l}owski and Jan Pulikowski},
     title = {Smooth {Actions} of $p${-Toral} {Groups} on $\mathbb Z${-Acyclic} {Manifolds}},
     journal = {Informatics and Automation},
     pages = {283--290},
     publisher = {mathdoc},
     volume = {305},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2019_305_a14/}
}
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Krzysztof M. Pawałowski; Jan Pulikowski. Smooth Actions of $p$-Toral Groups on $\mathbb Z$-Acyclic Manifolds. Informatics and Automation, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 283-290. http://geodesic.mathdoc.fr/item/TRSPY_2019_305_a14/