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Furthermore we show that every positive real number is equal to the Novikov-Shubin invariant of some element of the real group ring of Z_2 \\wr Z. Finally we show that the l2-Betti number of a matrix over the integral group ring of the group Z_p \\wr Z, p>1, can be irrational, and so the groups Z_p \\wr Z become the simplest known groups which give rise to irrational l2-Betti numbers."},"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":"1009.0229","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-09-01T17:40:58Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"c1ca584efd3c23307536ca806adfdf873deefdd65799637bd1c7caf6058e900e","abstract_canon_sha256":"2f98702994af265b44482c024e815842d2d5a120960c32ae3d01d5e584e29e09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:52.667471Z","signature_b64":"F866+FyoeSA87BBmOwYwOJMLT27w7ZFcLHVHWYAS5o92abPjFS+F/puc1/X3tPvlH3KCMnpleEmG2OIeJp+pCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea0898cabe8e4c58face4262795fbffb8f66a603f58bbc3f08aafaf6ae8a440a","last_reissued_at":"2026-05-18T02:17:52.666714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:52.666714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Irrational l2-invariants arising from the lamplighter group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"{\\L}ukasz Grabowski","submitted_at":"2010-09-01T17:40:58Z","abstract_excerpt":"We show that the Novikov-Shubin invariant of an element of the integral group ring of the lamplighter group Z_2 \\wr Z can be irrational. 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