Measure expanding actions, expanders and warped cones

Vigolo, Federico

doi:10.1090/tran/7368

Measure expanding actions, expanders and warped cones
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by Federico Vigolo PDF

Trans. Amer. Math. Soc. 371 (2019), 1951-1979 Request permission

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 constructing 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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