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The existence depends on the $L^2$-Betti numbers of $\\Gamma$, its subgroups and of a uniform lattice of $\\Isom(X)$. As an application, we show the existence of a uniform positive lower bound on the Cheeger constant of any manifold of the form $\\H^4/\\Gamma$ where $\\H^4$ is real hyperbolic 4-space and $\\Gamma<\\Isom(\\H^4)$ is discrete and isomorphic to a subgroup"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1303.5963","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-24T16:20:37Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"5a1b6112e5d7db379673133779eb64e9c777d2a3d43410a72c13dea737729fa0","abstract_canon_sha256":"39aaf42502fc2761280fad3dce8d55833cf3f5ccbd5649f7018741551f558ca9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:15.323936Z","signature_b64":"nOJOte7Uq91GeHgjh8hoez714Y4Edb2hkC27lUf2SWslWmSdHRrL6TagVyy7EYjx/MMsY2dIcfS578/ufn8JAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78bc9cc87f541276b46adb87e92bb8ab3708b1306e2eb93798d09d09f7ed153e","last_reissued_at":"2026-05-18T01:28:15.323172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:15.323172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cheeger constants and $L^2$-Betti numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GT","authors_text":"Lewis Bowen","submitted_at":"2013-03-24T16:20:37Z","abstract_excerpt":"We prove the existence of positive lower bounds on the Cheeger constants of manifolds of the form $X/\\Gamma$ where $X$ is a contractible Riemannian manifold and $\\Gamma<\\Isom(X)$ is a discrete subgroup, typically with infinite co-volume. 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