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arXiv · 2302.00468

LS-category and topological complexity of several families of fibre bundles

Navnath Daundkar·Soumen Sarkar
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Abstract

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 $3$-dimensional Klein bottle. 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 reckon 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.

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Navnath Daundkar, Soumen Sarkar. 2023-02-01. LS-category and topological complexity of several families of fibre bundles. https://arxiv.org/abs/2302.00468

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