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arXiv · 1610.05837

Measure expanding actions, expanders and warped cones

Federico Vigolo
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Abstract

We define a way of approximating actions on measure spaces using finite graphs; we then show that in quite general settings these graphs form a family of expanders if and only if the action is expanding in measure. This provides a somewhat unified approach to construct expanders. We also show that the graphs we obtain are uniformly quasi-isometric to the level sets of warped cones. This way we can also prove non-embeddability results for the latter and restate an old conjecture of Gamburd-Jakobson-Sarnak.

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Federico Vigolo. 2018-07-30. Measure expanding actions, expanders and warped cones. https://doi.org/10.1090/tran%2F7368

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