Pith Number

pith:RXMZPW3X

pith:2026:RXMZPW3XMHO3XEHJZPIJ5BUI4P

not attested not anchored not stored refs resolved

Amenability and comparison for \'etale groupoids with polynomial growth

Are Austad, Christian B\"onicke

Second-countable étale groupoids with polynomial growth are topologically amenable.

arxiv:2605.16013 v1 · 2026-05-15 · math.DS · math.OA

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Claims

C1strongest claim

We show that any second-countable étale groupoid with polynomial growth is topologically amenable. If its unit space is compact and metrizable, we show that the groupoid has weak m-comparison. Thus if the groupoid is also ample and minimal, it satisfies Matui's AH conjecture.

C2weakest assumption

The polynomial growth condition on the groupoid, together with second-countability and the étale property, is assumed to be sufficient to construct sequences witnessing topological amenability (or weak m-comparison) without additional restrictions on the groupoid structure.

C3one line summary

Second-countable étale groupoids with polynomial growth are topologically amenable, and under compactness, metrizability, ampleness and minimality they satisfy weak m-comparison and Matui's AH conjecture.

References

44 extracted · 44 resolved · 0 Pith anchors

[1] 2016 , Eprint = 2016

[2] Fiberwise amenability of ample \'

[3] Williams, Dana P. , title =. 2019 , publisher =. doi:10.1090/surv/241 , keywords = 2019 · doi:10.1090/surv/241

[4] Anantharaman-Delaroche, C. and Renault, J. , TITLE =. 2000 , PAGES = 2000

[5] On a class of singular measures satisfying a strong annular decay condition , JOURNAL = 2019

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:49.110368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8dd997db7761ddbb90e9cbd09e8688e3c79181615dddfbc4a55c348ea4fec41f

Aliases

arxiv: 2605.16013 · arxiv_version: 2605.16013v1 · doi: 10.48550/arxiv.2605.16013 · pith_short_12: RXMZPW3XMHO3 · pith_short_16: RXMZPW3XMHO3XEHJ · pith_short_8: RXMZPW3X

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RXMZPW3XMHO3XEHJZPIJ5BUI4P \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8dd997db7761ddbb90e9cbd09e8688e3c79181615dddfbc4a55c348ea4fec41f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "953e1704aeec6895db680cdf79ddbb0dfd916e5ae2733c2912a310b99f0f679d",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-15T14:45:39Z",
    "title_canon_sha256": "bf965fbde38de8db3ca88372f96d3dcdb1a22f085d6c1b7bd309a2e11b81618c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16013",
    "kind": "arxiv",
    "version": 1
  }
}