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On equivariant and invariant topological complexity of smooth $ \mathbb{Z}/_p$-spheres


Authors: Zbigniew Błaszczyk and Marek Kaluba
Journal: Proc. Amer. Math. Soc. 145 (2017), 4075-4086
MSC (2010): Primary 57S17, 57S25; Secondary 55M30
DOI: https://doi.org/10.1090/proc/13528
Published electronically: March 27, 2017
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Abstract: We investigate equivariant and invariant topological complexity of spheres endowed with smooth non-free actions of cyclic groups of prime order. We prove that semilinear $ \mathbb{Z}/_{\!p}$-spheres have both invariants either $ 2$ or $ 3$ and calculate exact values in all but two cases. On the other hand, we exhibit examples which show that these invariants can be arbitrarily large in the class of smooth $ \mathbb{Z}/_{\!p}$-spheres.


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Additional Information

Zbigniew Błaszczyk
Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
Email: blaszczyk@amu.edu.pl

Marek Kaluba
Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland – and – Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland
Email: kalmar@amu.edu.pl

DOI: https://doi.org/10.1090/proc/13528
Keywords: Equivariant topological complexity, homology sphere, smooth action, Lusternik--Schnirelmann $G$\nobreakdash-category.
Received by editor(s): March 6, 2015
Received by editor(s) in revised form: September 30, 2016
Published electronically: March 27, 2017
Additional Notes: The authors were supported by the National Science Centre grants: 2014/12/S/ST1/00368 and 2015/19/B/ST1/01458, respectively.
Communicated by: Kevin Whyte
Article copyright: © Copyright 2017 American Mathematical Society