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Thesis

Geometry of actions, expanders and warped cones

Abstract:

In this thesis we introduce a notion of graphs approximating actions of finitely generated groups on metric and measure spaces. We systematically investigate expansion properties of said graphs and we prove that a sequence of graphs approximating a fixed action ρ forms a family of expanders if and only if ρ is expanding in measure. This enables us to rely on a number of known results to construct numerous new families of expander (and superexpander) graphs.

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Division:
MPLS
Department:
Mathematical Institute
Role:
Author

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Supervisor
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Funding agency for:
Vigolo, F
Grant:
J.T.Hamilton Scholarship
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford
Language:
English
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UUID:
uuid:0b094203-6f94-4b3b-826e-c8b1ac6203b8
Deposit date:
2018-10-03

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