标题： 图的可分同调与Whitehead复形 显示英文标题

标题： Separable homology of graphs and the Whitehead complex

摘要： 我们引入了Whitehead复形，这是一个与玫瑰的有限正则覆盖相关的1-复形，并证明当且仅当相关覆盖的基本群由其与$\mathbf{F}_n$中真自由因子的元素的交集生成时，该复形是连通的。 如果相关覆盖对应于$\mathbf{F}_n$的一个特征子群，则Whitehead复形在$\mathrm{Out}(\mathbf{F}_n)$的作用下具有等距作用。 我们证明了玫瑰的Whitehead复形具有无限直径且非双曲，这意味着它与自由分裂复形或自由因子复形不拟等距。 显示英文摘要

摘要： We introduce the Whitehead complex, a one-complex associated to a finite regular cover of the rose and show that it is connected if and only if the fundamental group of the associated cover is generated by its intersection with the set of elements in proper free factors of $\mathbf{F}_n$. The Whitehead complex admits an action of $\mathrm{Out}(\mathbf{F}_n)$ by isometries if the associated cover corresponds to a characteristic subgroup of $\mathbf{F}_n$. We prove that the Whitehead complex of the rose has infinite diameter and is nonhyperbolic, implying it is not quasi-isometric to the free splitting complex or the free factor complex.