Pushing fillings in right‐angled Artin groups
Pushing fillings in right‐angled Artin groups
复制标题
将填充物推入直角 Artin 组中
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Robert Young
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文献类型：
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作者：
Aaron Abrams;N. Brady;Pallavi Dani;M. Duchin;Robert Young
我们得到了直角Artin群（RAAG）的高发散函数的界，发现RAAG的k维发散由r2 k +2上界。这些发散函数，以前定义为阿达玛流形在无穷远处测量等周性质，在这里定义为群的拟等距不变量族。我们还证明了Bestvina-Brady群的k阶Dehn函数的上界为V（2k+2）/k，并构造了一类称为orthoplex群的RAAG，证明了这些上界都是尖锐的.
We obtain bounds on the higher divergence functions of right‐angled Artin groups (RAAGs), finding that the k‐dimensional divergence of a RAAG is bounded above by r2k+2. These divergence functions, previously defined for Hadamard manifolds to measure isoperimetric properties at infinity, are defined here as a family of quasi‐isometry invariants of groups. We also show that the kth order Dehn function of a Bestvina–Brady group is bounded above by V(2k+2)/k and construct a class of RAAGs called orthoplex groups which show that each of these upper bounds is sharp.