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We give an algebraic formula for the radial index of a 1-form on the real quotient $W$. It is shown that this index is equal to the signature of the restriction of the residue pairing to the $G$-invariant part $\\Omega^G_\\omega$ of $\\Omega_\\omega= \\Omega^n_{\\mathbb{R}^n,0}/\\omega \\wedge \\Omega^{n-1}_{\\mathbb{R}^n,0}$. For a $G$-invariant function $f$, one has the so-called quantu"},"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":"1708.09219","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-30T11:32:26Z","cross_cats_sorted":[],"title_canon_sha256":"75e4cee88ce89eb871a6ea905901827d5ff41b13dc588501aafe43cd2560902a","abstract_canon_sha256":"74aea2b0a13925499018a9cbd4a9b93bd95d98a65f799ce671d43a05c5b0a3b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:20.566446Z","signature_b64":"exdv+SJ/3pCooBnVB4BnZKgAxfl+2mSOZkXN290Ee0uMQhEDmm+82wHvaLQGHtA5rG7JtO22UUWmxOeGaAqbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53d3b0284e1db35c5386c5649c49dcb5b4819c7f9cd7b941103dbb0b45b74cdb","last_reissued_at":"2026-05-18T00:36:20.565925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:20.565925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An algebraic formula for the index of a 1-form on a real quotient singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sabir M. Gusein-Zade, Wolfgang Ebeling","submitted_at":"2017-08-30T11:32:26Z","abstract_excerpt":"Let a finite abelian group $G$ act (linearly) on the space $\\mathbb{R}^n$ and thus on its complexification $\\mathbb{C}^n$. Let $W$ be the real part of the quotient $\\mathbb{C}^n/G$ (in general $W \\neq \\mathbb{R}^n/G$). We give an algebraic formula for the radial index of a 1-form on the real quotient $W$. It is shown that this index is equal to the signature of the restriction of the residue pairing to the $G$-invariant part $\\Omega^G_\\omega$ of $\\Omega_\\omega= \\Omega^n_{\\mathbb{R}^n,0}/\\omega \\wedge \\Omega^{n-1}_{\\mathbb{R}^n,0}$. 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