群图的Dehn函数的布朗定理
A Brown Theorem for Dehn functions of graphs of groups
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中文总结 AI 辅助
该研究针对在单连通CW复形上满足特定条件的群，证明了其Dehn函数的上界，给出了有限性性质布朗定理的Dehn函数类似结果，回答了Zaremsky的问题，并得到了高阶Dehn函数的对应结果。
中文摘要 AI 辅助
我们证明了，当群G在单连通CW复形X上实现胞腔、紧且无逆作用，且X要么是树，要么每个2-胞腔的稳定子在其边界每条边的稳定子中具有有限指数时，可通过顶点稳定子的Dehn函数、X的Dehn函数以及边稳定子的畸变来给出群G的Dehn函数的上界。这为有限性性质的布朗定理提供了Dehn函数的类似结果，并在这些情形下回答了Zaremsky的一个问题。我们还证明了当X是树时，高阶Dehn函数的类似结果。
英文摘要
We prove an upper bound on the Dehn function of a group $G$ acting cellularly, cocompactly, and without inversions on a simply connected CW complex $X$ in terms of the Dehn functions of the vertex stabilizers, the Dehn function of $X$, and the distortion of the edge stabilizers, provided that $X$ is either a tree or the stabilizer of each $2$-cell has finite index in the stabilizer of every edge in its boundary. This provides a Dehn function analogue of Brown's Theorem for finiteness properties and an answer to a question of Zaremsky in these cases. We also prove analogues of our result for higher Dehn functions when $X$ is a tree.
