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
MathSciNet review:
3665058
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Abstract | References | Similar Articles | Additional Information
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
Keywords:
Equivariant topological complexity,
homology sphere,
smooth action,
Lusternik–Schnirelmann $G$-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
