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Speaker:

David Hume
Affiliation:

Oxford
Date:

Thu, 18/10/2012 - 16:30 - 17:30
Location:

MPIM Lecture Hall
Parent event:

Oberseminar Differentialgeometrie We prove that quasi-trees of spaces satisfying the axiomatisation given by Bestvina, Bromberg and Fujiwara are quasi-isometric to tree-graded spaces in the sense of Dru\c{t}u and Sapir. As a corollary we deduce that mapping class groups quasi-isometrically embed into a finite product of tree-graded spaces. This gives bounds on compression exponent and guarantees finite Assouad-Nagata dimension. Moreover, using results of Buyalo and Masur-Minsky we prove that curve complexes embed into a finite product of trees, which we use to complete the theorem stated in the title."

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