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Median structures on asymptotic cones and homomorphisms into mapping class groups

Abstract:

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 ...

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Publication status:
Published

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Publisher copy:
10.1112/plms/pdq025
Journal:
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY More from this journal
Volume:
102
Issue:
3
Pages:
503-554
Publication date:
2008-10-29
DOI:
EISSN:
1460-244X
ISSN:
0024-6115
Language:
English
Keywords:
Pubs id:
pubs:127297
UUID:
uuid:1cb3709e-35eb-4483-8672-e9352c90d2b9
Local pid:
pubs:127297
Source identifiers:
127297
Deposit date:
2012-12-19

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