Median structures on asymptotic cones and homomorphisms into mapping class groups - Mathematics > Geometric TopologyReport as inadecuate




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Abstract: The main goal of this paper is a detailed study of asymptotic cones of themapping class groups. In particular, we prove that every asymptotic cone of amapping class group has a bi-Lipschitz equivariant embedding into a product ofreal trees, sending limits of hierarchy paths onto geodesics, and with image amedian subspace. One of the applications is that a group with Kazhdan-sproperty T can have only finitely many pairwise non-conjugate homomorphismsinto a mapping class group. We also give a new proof of the rank conjecture ofBrock and Farb previously proved by Behrstock and Minsky, and independently byHamenstaedt.



Author: J. Behrstock, C. Drutu, M. Sapir

Source: https://arxiv.org/







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