LS-category and topological complexity of several families of fibre bundles

2023/02/01 by Daundkar, Navnath, Sarkar, Soumen · 1 citation
#55M30 #55P15 #57N65 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.00468

Abstract

In this paper, we study 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 3-dimensional Klein bottle. We describe the cohomology rings of several classes of generalized projective product spaces with ℤ₂-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 ℤ₂-action.

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