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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).
Received: August 30, 2018 Revised: January 11, 2019 Accepted: March 16, 2019
Citation:
Krzysztof M. Pawałowski, Jan Pulikowski, “Smooth Actions of $p$-Toral Groups on $\mathbb Z$-Acyclic Manifolds”, Algebraic topology, combinatorics, and mathematical physics, Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 75th birthday, Trudy Mat. Inst. Steklova, 305, Steklov Math. Inst. RAS, Moscow, 2019, 283–290; Proc. Steklov Inst. Math., 305 (2019), 262–269
Linking options:
https://www.mathnet.ru/eng/tm3987https://doi.org/10.4213/tm3987 https://www.mathnet.ru/eng/tm/v305/p283
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Abstract page: | 308 | Full-text PDF : | 30 | References: | 35 | First page: | 11 |
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