{"paper":{"title":"On $d$-invariants and generalised Kanenobu knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Marco Marengon","submitted_at":"2014-12-10T20:07:03Z","abstract_excerpt":"We prove that for particular infinite families of $L$-spaces, arising as branched double covers, the $d$-invariants defined by Ozsv\\'ath and Szab\\'o are arbitrarily large and small. As a consequence, we generalise a result by Greene and Watson by proving, for every odd number $\\Delta \\geq 5$, the existence of infinitely many non-quasi-alternating homologically thin knots with determinant $\\Delta^2$, and a result by Hoffman and Walsh concerning the existence of hyperbolic weight $1$ manifolds that are not surgery on a knot in $S^3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3433","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}