Stable commutator length in Baumslag–Solitar groups and quasimorphisms for tree actions
Stable commutator length in Baumslag–Solitar groups and quasimorphisms for tree actions
复制标题
Baumslag-Solitar 群中的稳定换向器长度和树作用的拟同构
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Joel Louwsma
中科院分区：
文献类型：
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作者：
Matt Clay;Max Forester;Joel Louwsma
本文分为两部分，关于Baumslag-Solitar群和一般G-树。
在第一部分中，我们建立了Baumslag-Solitar群中稳定交换子长度（scl）的界。对于某类元素，我们进一步证明了scl是可计算的，并且取有理数值。我们还确定正是这些元素承认极值曲面。
在第二部分中，我们建立了任意群的合适元作用于树的scl的一个泛下界为1/12。这是通过构造有效的拟同构来实现的。在群BS（2，3）中的计算表明，这是最好的可能的泛界，从而回答了Calegari和Fujiwara的一个问题。我们还建立了acyllinobutter树行动的scl界限。
回到Baumslag-Solitar群，我们证明了它们的scl谱有一个均匀的间隙：没有元素有scl在区间（0，1/12）。
This paper has two parts, on Baumslag-Solitar groups and on general G-trees.
In the first part we establish bounds for stable commutator length (scl) in Baumslag-Solitar groups. For a certain class of elements, we further show that scl is computable and takes rational values. We also determine exactly which of these elements admit extremal surfaces.
In the second part we establish a universal lower bound of 1/12 for scl of suitable elements of any group acting on a tree. This is achieved by constructing efficient quasimorphisms. Calculations in the group BS(2,3) show that this is the best possible universal bound, thus answering a question of Calegari and Fujiwara. We also establish scl bounds for acylindrical tree actions.
Returning to Baumslag-Solitar groups, we show that their scl spectra have a uniform gap: no element has scl in the interval (0, 1/12).