渐近锥面上的中值结构与到映射类群的同态
Median structures on asymptotic cones and homomorphisms into mapping class groups
摘要：
本文的主要目的是详细研究映射类群的渐近锥面。特别是，我们证明了每一个渐近锥面的映射类群有一个双Lipschitz等变嵌入到一个产品的真正的树，发送限制的层次路径上测地线，并与图像的中值子空间。其中一个应用是具有Kazhdan性质的群（T）只能有1/2个两两非共轭同态到一个映射类群中。我们还给出了一个新的证明秩猜想的Brock和Farb（以前证明的Behrstock和明斯基，并独立Hamenstaedt）。
英文摘要：
The main goal of this paper is a detailed study of asymptotic cones of the mapping class groups. In particular, we prove that every asymptotic cone of a mapping class group has a bi-Lipschitz equivariant embedding into a product of real trees, sending limits of hierarchy paths onto geodesics, and with image a median subspace. One of the applications is that a group with Kazhdan's property (T) can have only finitely many pairwise non-conjugate homomorphisms into a mapping class group. We also give a new proof of the rank conjecture of Brock and Farb (previously proved by Behrstock and Minsky, and independently by Hamenstaedt).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
