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Distributional Topological Complexity of groups

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arxiv 2404.03041 v2 pith:32I7OPUG submitted 2024-04-03 math.GT

Alexander Dranishnikov This is my paper · ORCID
classification math.GT
keywords groupscitegammasurfacescomplexitycomputecomputedcyclic
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abstract

We study numerical invariants $d\TC(\Gamma)$ and $d\cat(\Gamma)$ of groups recently introduced in \cite{DJ} and independently in \cite{KW}. 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 \cite{DJ}). We prove the formula $$d\TC(G\ast H)=\max\{d\TC (G),d\TC (H), \cd(G\times H)\}$$ for torsion free groups.

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Cited by 1 Pith paper

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  1. Bochner-type theorems for distributional category

    math.AT 2025-05 conditional novelty 6.0 of 10

    Distributional category bounds Betti numbers, Gottlieb group rank, and macroscopic dimension, with equality forcing torus or flat manifold structure.

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