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Cross ratios on cube complexes and length-spectrum rigidity

Abstract:

We prove two versions of the marked length-spectrum rigidity conjecture for a large class of non-positively curved spaces: CAT(0) cube complexes. Under weak assumptions, we show that proper cocompact actions of Gromov hyperbolic groups on CAT(0) cube complexes are fully determined by their combinatorial length functions. If the cube complexes are irreducible and have the geodesic extension property, the same result holds for non-proper, non-cocompact actions of arbitrary groups.

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Division:
MPLS
Department:
Mathematical Institute
Role:
Author

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Role:
Supervisor
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Funding agency for:
Fioravanti, E
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford
Language:
English
UUID:
uuid:2967b9ec-05ad-4419-b5c0-1fa5324d2f93
Deposit date:
2019-09-23

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