Is the group of interval exchange transformations amenable?

Decide whether the group of interval exchange transformations of the circle is amenable.

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1	{
2	"domain": "mathematics",
3	"topics": [
4	"algebra",
5	"analysis"
6	],
7	"type": "proof",
8	"source": {
9	"key": "aimpl",
10	"name": "AIM Problem Lists",
11	"url": "http://aimpl.org/amenablediscrete/2/",
12	"id": "amenablediscrete 2.2",
13	"curator": "American Institute of Mathematics",
14	"status": "open",
15	"as_of": "2026-10-20",
16	"catalog": "0521c19bbd38"
17	},
18	"review": true,
19	"approval": "first-time"
20	}