Geodesic
LS-category and topological complexity of several families of fibre bundles
Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 273-295.

Voir la notice de l'article provenant de la source International Press of Boston

In this paper, we study the 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 a $3$-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.
DOI : 10.4310/HHA.2024.v26.n2.a14
Classification : 55M30, 55N10, 55R10
Keywords: LS-category, topological complexity, fibre bundle, projective product space 
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     title = {LS-category and topological complexity of several families of fibre bundles},
     journal = {Homology, homotopy, and applications},
     pages = {273--295},
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     year = {2024},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n2.a14/}
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Navnath Daundkar; Soumen Sarkar. LS-category and topological complexity of several families of fibre bundles. Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 273-295. doi : 10.4310/HHA.2024.v26.n2.a14. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n2.a14/

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