群的分布拓扑复杂度
Distributional Topological Complexity of groups
AI总结：
本文研究了群的两个数值不变量$d\TC(Γ)$和$d\cat(Γ)$，计算了有限循环群及不可定向曲面的$d\TC$值，并为无挠群证明了相关的$d\TC$计算公式。
摘要：
我们研究群在\cite{DJ}及独立在\cite{KW}中引入的数值不变量$d\TC(Γ)$和$d\cat(Γ)$。计算了素数$p$下有限循环群$\mathbb Z_p$及亏格$g>3$不可定向曲面的$d\TC$（可定向曲面已在\cite{DJ}中计算）。证明了无挠群公式$d\TC(G\ast H)=\max\{d\TC(G),d\TC(H),\cd(G\times H)\}$。
英文摘要：
We study numerical invariants $d\TC(Γ)$ and $d\cat(Γ)$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
