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On Lusternik–Schnirelmann category and topological complexity of non-k-equal manifolds

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Abstract

We compute the Lusternik–Schnirelmann category and all the higher topological complexities of non-k-equal manifolds \(M_d^{(k)}(n)\) for certain values of d, k and n. This includes instances where \(M_d^{(k)}(n)\) is known to be rationally non-formal. The key ingredient in our computations is the knowledge of the cohomology ring \(H^*(M_d^{(k)}(n))\) as described by Dobrinskaya and Turchin. A fine tuning comes from the use of obstruction theory techniques.

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Acknowledgements

The second author was supported by a Conacyt PhD scholarship.

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Author notes

  1. José Luis León-Medina contributed equally to this work.

Authors and Affiliations

  1. Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del I.P.N., Av. Instituto Politécnico Nacional No. 2508, San Pedro Zacatenco, 07360, Mexico City, Mexico

    Jesús González & José Luis León-Medina

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  1. Jesús González
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  2. José Luis León-Medina
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Correspondence to Jesús González.

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Communicated by Martin Raussen.

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González, J., León-Medina, J.L. On Lusternik–Schnirelmann category and topological complexity of non-k-equal manifolds. J. Homotopy Relat. Struct. 17, 217–231 (2022). https://doi.org/10.1007/s40062-022-00304-z

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  • DOI: https://doi.org/10.1007/s40062-022-00304-z

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