On distributional topological complexity of groups and manifolds

2025/09/20 by Dranishnikov, Alexander
#55M30 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2509.16759

Abstract

We prove the equality \dTC(Γ)=\TC(Γ) for distributional topological complexity of torsion free hyperbolic and of torsion free nilpotent groups. For the distributional topological complexity of lens spaces we prove the inequality \dTC(Lⁿ_p)≤ 2p-1 and for the distributional LS-category the inequality d\cat(Lⁿ_p)≤ p-1 which turns into equality for prime p and n>p. We use these inequalities to bring counter-examples to the product formula for d\cat and \dTC.

Citations

• On the complexity of parametrized motion planning algorithms
• On distributional one-category, diagonal distributional complexity, and related invariants
• Bochner-type theorems for distributional category
• On the analog category of finite groups
• Distributional Topological Complexity of groups
• Analog category and complexity
• On dimension of product of groups
• On the topological complexity of aspherical spaces
• Symmetric Joins and Weighted Barycenters
• Survey on Classifying Spaces for Families of Subgroups
• Topological robotics: motion planning in projective spaces
• Topological complexity of motion planning

Related

• Distributional Topological Complexity of groups
• On distributional one-category, diagonal distributional complexity, and related invariants
• On the topological complexity of toral relatively hyperbolic groups
• On topological complexity of hyperbolic groups
• Intertwining category and complexity