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Embedding mapping class groups into a finite product of trees

Abstract:

We prove the equivalence between a relative bottleneck property and being quasi-isometric to a tree-graded space. As a consequence, we deduce that the quasi-trees of spaces defined axiomatically by Bestvina-Bromberg-Fujiwara are quasi-isometric to tree-graded spaces. Using this we prove that mapping class groups quasi-isometrically embed into a finite product of simplicial trees. In particular, these groups have finite Assouad–Nagata dimension, direct embeddings exhibiting ℓp compression expo...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.4171/GGD/410

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Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
Publisher:
European Mathematical Society Publisher's website
Journal:
Groups, Geometry, and Dynamics Journal website
Volume:
11
Issue:
2
Pages:
613–647
Publication date:
2017-01-01
Acceptance date:
2017-01-24
DOI:
EISSN:
1661-7215
ISSN:
1661-7207
Pubs id:
pubs:701587
URN:
uri:33713d78-9f1e-422c-804d-389cc3f0e3aa
UUID:
uuid:33713d78-9f1e-422c-804d-389cc3f0e3aa
Local pid:
pubs:701587
Paper number:
2

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