{"paper":{"title":"Width is not additive","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Maggy Tomova, Ryan Blair","submitted_at":"2010-05-09T02:39:53Z","abstract_excerpt":"We develop a construction suggested by Scharlemann and Thompson to obtain an infinite family of pairs of knots $K_{\\alpha}$ and $K'_{\\alpha}$ so that $w(K_{\\alpha} # K'_{\\alpha})=max{w(K_{\\alpha}), w(K'_{\\alpha})}$. This is the first known example of a pair of knots such that $w(K#K')<w(K)+w(K')-2$ and it establishes that the lower bound $w(K#K')\\geq max{w(K),w(K')}$ obtained by Scharlemann and Schultens is best possible. Furthermore, the knots $K_{\\alpha}$ provide an example of knots where the number of critical points for the knot in thin position is greater than the number of critical point"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1359","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"}