LS-category and topological complexity of Milnor manifolds and corresponding generalized projective product spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913189198823424 |
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| author | Daundkar, Navnath |
| author_facet | Daundkar, Navnath |
| contents | Milnor manifolds are a class of certain codimension-$1$ submanifolds of the product of projective spaces. In this paper, we study the LS-category and topological complexity of these manifolds. We determine the exact value of the LS-category and in many cases, the topological complexity of these manifolds. We also obtain tight bounds on the topological complexity of these manifolds. It is known that Milnor manifolds admit $\mathbb{Z}_2$ and circle actions. We compute bounds on the equivariant LS-category and equivariant topological complexity of these manifolds. Finally, we describe the mod-$2$ cohomology rings of some generalized projective product spaces corresponding to Milnor manifolds and use this information to compute the bound on LS-category and topological complexity of these spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03333 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | LS-category and topological complexity of Milnor manifolds and corresponding generalized projective product spaces Daundkar, Navnath Algebraic Topology 55M30, 55P15, 57N65 Milnor manifolds are a class of certain codimension-$1$ submanifolds of the product of projective spaces. In this paper, we study the LS-category and topological complexity of these manifolds. We determine the exact value of the LS-category and in many cases, the topological complexity of these manifolds. We also obtain tight bounds on the topological complexity of these manifolds. It is known that Milnor manifolds admit $\mathbb{Z}_2$ and circle actions. We compute bounds on the equivariant LS-category and equivariant topological complexity of these manifolds. Finally, we describe the mod-$2$ cohomology rings of some generalized projective product spaces corresponding to Milnor manifolds and use this information to compute the bound on LS-category and topological complexity of these spaces. |
| title | LS-category and topological complexity of Milnor manifolds and corresponding generalized projective product spaces |
| topic | Algebraic Topology 55M30, 55P15, 57N65 |
| url | https://arxiv.org/abs/2303.03333 |