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

2023/03/06 by Daundkar, Navnath
#55M30 #55P15 #57N65 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.03333

Abstract

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 ℤ₂ 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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