On generalized projective product spaces and Dold manifolds

Sarkar, Soumen; Zvengrowski, Peter

doi:10.4310/hha.2022.v24.n2.a13

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…Sarkar and Zvengrowski [20] defined the generalized projective product spaces and studied topological aspects of some of its classes. The author and Sarkar [5], obtained upper bounds on the LS-category and topological complexity of generalized projective product spaces (see [5, Proposition 2.4, Proposition 2.5]).…”

Section: G Mmentioning

confidence: 99%

“…Next, we define another class of generalized projective product spaces related to Milnor manifolds and compute bounds on LS-category and topological complexity of these spaces. Let N = S n 1 × • • • × S n k be the product of unit spheres with the involution τ determined by the antipodal involution on each factor S n j for 1 ≤ j ≤ k. Now we recall the involution τ j on S n j defined in [20,Example 3.1].…”

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LS-category and topological complexity of Milnor manifolds and corresponding generalized projective product space

Daundkar¹

2023

Preprint

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NAVNATH DAUNDKAR A. 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 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.

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Section: G Mmentioning

confidence: 99%

mentioning

confidence: 99%

LS-category and topological complexity of Milnor manifolds and corresponding generalized projective product space

Daundkar¹

2023

Preprint

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Equivariant LS-Category and Topological Complexity of Product of Several Manifolds

Karthika,

Renukadevi

2024

Lecture Notes in Networks and Systems

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Various topological complexities of small covers and real Bott manifolds

Brahma,

Naskar,

Sarkar

et al. 2023

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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In this paper, we compute the LS-category and equivariant LS-category of a small cover and its real moment angle manifold. We calculate a tight lower bound for the topological complexity of many small covers over a product of simplices. Then we compute symmetric topological complexity of several small covers over a product of simplices. We calculate the LS one-category of real Bott manifolds and infinitely many small covers.

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On generalized projective product spaces and Dold manifolds

Cited by 3 publications

References 13 publications

LS-category and topological complexity of Milnor manifolds and corresponding generalized projective product space

LS-category and topological complexity of Milnor manifolds and corresponding generalized projective product space

Equivariant LS-Category and Topological Complexity of Product of Several Manifolds

Various topological complexities of small covers and real Bott manifolds

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