Discrete fundamental groups of warped cones and expanders

In this paper we compute the discrete fundamental groups of warped cones. As an immediate consequence, this allows us to show that there exist coarsely simply-connected expanders and superexpanders. This also provides a strong coarse invariant of warped cones and implies that many warped cones canno...

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Bibliographic Details
Published in:Mathematische annalen 2019-02, Vol.373 (1-2), p.355-396
Main Author: Vigolo, Federico
Format: Article
Language:English
Subjects:
Cones
Expanders
Mathematics
Mathematics and Statistics
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Summary:In this paper we compute the discrete fundamental groups of warped cones. As an immediate consequence, this allows us to show that there exist coarsely simply-connected expanders and superexpanders. This also provides a strong coarse invariant of warped cones and implies that many warped cones cannot be coarsely equivalent to any box space.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-018-1768-7