{"paper":{"title":"Blobbed topological recursion: properties and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ga\\\"etan Borot, Sergey Shadrin","submitted_at":"2015-02-03T19:51:34Z","abstract_excerpt":"We study the set of solutions $(\\omega_{g,n})_{g \\geq 0,n \\geq 1}$ of abstract loop equations. We prove that $\\omega_{g,n}$ is determined by its purely holomorphic part: this results in a decomposition that we call \"blobbed topological recursion\". This is a generalization of the theory of the topological recursion, in which the initial data $(\\omega_{0,1},\\omega_{0,2})$ is enriched by non-zero symmetric holomorphic forms in $n$ variables $(\\phi_{g,n})_{2g - 2 + n > 0}$. In particular, we establish for any solution of abstract loop equations: (1) a graphical representation of $\\omega_{g,n}$ in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00981","kind":"arxiv","version":2},"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"}