Smooth Actions of $p$-Toral Groups on $\mathbb Z$-Acyclic Manifolds

Krzysztof M. Pawałowski, Jan Pulikowski

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Collegium Mathematicum, ul. Umultowska 87, 61-614 Poznań, Poland

Abstract: 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).

UDC: 515.14+515.16

Received: August 30, 2018
Revised: January 11, 2019
Accepted: March 16, 2019

DOI: 10.4213/tm3987

 English version: Proceedings of the Steklov Institute of Mathematics, 2019, 305, 262–269

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