Stable W-length
Stable W-length
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稳定的W长度
DOI：
10.1090/conm/560/11097
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Dongping Zhuang
中科院分区：
文献类型：
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作者：
Danny Calegari;Dongping Zhuang
本文研究了群的稳定W-长度，特别是当W等于n重交换子γ_n：= [x_1，[x_2，. [x_（n-1），x_n]].我们证明了在任何完全群中，对任意n ≥ 2和任意元素g，g的稳定换位子长度至少是g的稳定γ_n-长度的2^（2−n）倍。我们还建立了词γn和β_2：= [[x，y]，[z，w]]的Bavard对偶的类似。我们的证明利用了关于双不变度量的动词子群的渐近锥的几何性质。特别是，我们表明，适当的W，这些渐近锥包含一定的子群，赋范向量空间。
We study stable W-length in groups, especially for W equal to the n-fold commutator γ_n := [x_1, [x_2,...[x_(n−1), x_n]]....We prove that in any perfect group, for any n ≥ 2 and any element g, the stable commutator length of g is at least as big as 2^(2−n) times the stable γ_n-length of g. We also establish analogues of Bavard duality for words γn and for β_2 := [[x, y], [z,w]]. Our proofs make use of geometric properties of the asymptotic cones of verbal subgroups with respect to bi-invariant metrics. In particular, we show that for suitable W, these asymptotic cones contain certain subgroups that are normed vector spaces.