Navnath Daundkar, Soumen Sarkar
Published 2023-02-01Version 1
In this paper, we study upper bounds for the topological complexity of the total spaces of some classes of fibre bundles. We calculate a tight upper bound for the topological complexity of an $n$-dimensional Klein bottle. We also compute the exact value of the topological complexity of $2$ and $3$-dimensional Klein bottles. We describe the cohomology rings of several classes of generalized projective product spaces with $\mathbb{Z}_2$-coefficients. Then we study the LS-category and topological complexity of infinite families of generalized projective product spaces. We also compute the exact value of these invariants in many specific cases. We calculate the equivariant LS-category and equivariant topological complexity of several product spaces equipped with $\mathbb{Z}_2$-action.
LS-category and topological complexity of Milnor manifolds and corresponding generalized projective product spaces
Motion planning in polyhedral products of groups and a Fadell-Husseini approach to topological complexity
On the LS-category of homomorphisms of groups with torsion
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