Distributional Topological Complexity of groups

2024/04/03 by Dranishnikov, Alexander · 3 citations
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2404.03041

Abstract

We study numerical invariants d\TC(Γ) and d\cat(Γ) of groups recently introduced in \citeDJ and independently in \citeKW. We compute d\TC for finite cyclic groups \mathbb Z_p with prime p as well as for nonorientable surfaces of genus g>3 (for orientable surfaces it was computed in \citeDJ). We prove the formula d\TC(G∗ H)=max\d\TC (G),d\TC (H), \cd(G× H)\ for torsion free groups.

Cited by

• On the complexity of parametrized motion planning algorithms
• On distributional topological complexity of groups and manifolds
• On distributional one-category, diagonal distributional complexity, and related invariants

Related

• On distributional topological complexity of groups and manifolds
• The topological complexity of the free product
• On the topological complexity of toral relatively hyperbolic groups
• Topological complexity, fibrations and symmetry
• Asymptotic invariants, complexity of groups and related problems