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 Z / p \mathbb {Z}/_{\!p} -spheres have both invariants either 2 2 or 3 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 Z / p \mathbb {Z}/_{\!p} -spheres.
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