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Our first theorem is that if the first homology of $X$ is finite cyclic and $M$ is a Seifert fibered space with $N\\ge 3$ singular fibers, then $N\\ge 4$ if and only if the first homology of the universal abelian covering of $X$ is infinite. Our second theorem is that under an appropriate assumption on the Alexander polynomial of $K$, if $M$ is a Seifert fibered space, then $q=\\pm 1$ (i.e.\\ integral surgery)."},"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":"1708.09802","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-31T16:34:10Z","cross_cats_sorted":[],"title_canon_sha256":"e241840ee10a576bb6798253f24cfe81cbffba65f72eea691649eb48d4790d3a","abstract_canon_sha256":"f4131c6f015eacb738832aaa02089f3b146a3e785715f6386a4399483987af5c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:52.158915Z","signature_b64":"g5u5i8o0OhA2BF9D8hJylaB9wWvNQ8LyEdz7afCl3qgNC5LpmjsWHTZrcnjGUvZlotPSw3w8ylNf81fgGLyQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a434eb4739caaa80ee5737bfe07a02a9dd394d930231fa376f553692e159d137","last_reissued_at":"2026-05-18T00:20:52.158403Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:52.158403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Seifert surgery on knots via Reidemeister torsion and Casson-Walker-Lescop invariant III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Noriko Maruyama, Teruhisa Kadokami, Tsuyoshi Sakai","submitted_at":"2017-08-31T16:34:10Z","abstract_excerpt":"For a knot $K$ in a homology $3$-sphere $\\Sigma$, let $M$ be the result of $2/q$-surgery on $K$, and let $X$ be the universal abelian covering of $M$. 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