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Smooth Actions of p-Toral Groups on ℤ-Acyclic Manifolds

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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 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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Authors and Affiliations

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

    Krzysztof M. Pawałowski & Jan Pulikowski

Authors
  1. Krzysztof M. Pawałowski
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  2. Jan Pulikowski
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Corresponding authors

Correspondence to Krzysztof M. Pawałowski or Jan Pulikowski.

Additional information

Dedicated to Victor M. Buchstaber on the occasion of his 75th birthday

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Vol. 305, pp. 283–290.

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Pawałowski, K.M., Pulikowski, J. Smooth Actions of p-Toral Groups on ℤ-Acyclic Manifolds. Proc. Steklov Inst. Math. 305, 262–269 (2019). https://doi.org/10.1134/S0081543819030155

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  • DOI: https://doi.org/10.1134/S0081543819030155

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