{"paper":{"title":"On the fibres of Mishchenko-Fomenko systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.SG","authors_text":"Markus R\\\"oser, Peter Crooks","submitted_at":"2019-07-09T21:49:35Z","abstract_excerpt":"This work is concerned with Mishchenko and Fomenko's celebrated theory of completely integrable systems on a complex semisimple Lie algebra $\\mathfrak{g}$. Their theory associates a maximal Poisson-commutative subalgebra of $\\mathbb{C}[\\mathfrak{g}]$ to each regular element $a\\in\\mathfrak{g}$, and one can assemble free generators of this subalgebra into a moment map $F_a:\\mathfrak{g}\\rightarrow\\mathbb{C}^b$.\n  We examine the structure of fibres in Mishchenko--Fomenko systems, building on the foundation laid by Bolsinov, Charbonnel--Moreau, Moreau, and others. This includes proving that the cri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04429","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"}