{"paper":{"title":"Definable Topological Dynamics of $SL_2(\\mathbb{C}((t))$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Thomas Kirk","submitted_at":"2019-03-08T17:24:49Z","abstract_excerpt":"We initiate a study of definable topological dynamics for groups definable in metastable theories. Specifically, we consider the special linear group $G = SL_2$ with entries from $M = \\mathbb{C}((t))$; the field of formal Laurent series with complex coefficients. We prove such a group is not definably amenable, find a suitable group decomposition, and describe the minimal flows of the additive and multiplicative groups of $\\mathbb{C}((t))$. The main result is an explicit description of the minimal flow and Ellis Group of $(G(M),S_G(M))$ and we observe that this is not isomorphic to $G/G^{00}$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03570","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"}