{"paper":{"title":"The instanton homology of the $(-2,3,q)$ pretzel knots and computed bounding cochains in the pillowcase","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Bernd J. Wuebben","submitted_at":"2026-07-28T02:29:39Z","abstract_excerpt":"We prove that the reduced singular instanton knot homology of the pretzel knots $P(-2,3,q)$ has rank $q+2$ for every odd $q\\ge 3$: the Alexander polynomials of the family, computed in closed form by a skein recursion (Hironaka's Lehmer-like polynomials), give the lower bound $q+2$, and Manion's closed-form reduced Khovanov homology gives the matching upper bound. We then turn to the pillowcase (symplectic) side of the knot Atiyah-Floer program. In the immersed-curve combinatorial model of Herald-Kirk and Smith we reconstruct the pillowcase Lagrangians of the natural tangle decomposition of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26096","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.26096/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}