产生非平凡拟同构的树上的作用的特征
Characterising actions on trees yielding non-trivial quasimorphisms
摘要：
我们研究建设的拟同构群作用于树介绍了莫诺和沙洛姆，我们称之为中位数拟同构，特别是我们充分的行动树，产生非平凡的中位数拟同构。粗略地说，要么作用量在测地线上是高度传递的，它在边界上固定一个点，要么存在非平凡的中值拟同构的无限族。特别地，在最后一种情况下，群的第二有界上同调是无限维的向量空间。作为应用，我们证明了树的乘积中的余紧格只有平凡拟同构当且仅当两个因子上的投影闭包都是局部$\infty$ -传递的.
英文摘要：
We study the construction of quasimorphisms on groups acting on trees introduced by Monod and Shalom, that we call median quasimorphisms, and in particular we fully characterise actions on trees that give rise to non-trivial median quasimorphisms. Roughly speaking, either the action is highly transitive on geodesics, it fixes a point in the boundary, or there exists an infinite family of non-trivial median quasimorphisms. In particular, in the last case the second bounded cohomology of the group is infinite dimensional as a vector space. As an application, we show that a cocompact lattice in a product of trees only has trivial quasimorphisms if and only if both closures of the projections on the two factors are locally $\infty$-transitive.
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