{"paper":{"title":"Continuity of discrete homomorphisms of diffeomorphism groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GN","math.GR"],"primary_cat":"math.GT","authors_text":"Sebastian Hurtado","submitted_at":"2013-07-16T23:09:39Z","abstract_excerpt":"Let $M$ and $N$ be two closed $C^{\\infty}$ manifolds and let $\\text{Diff}_c(M)$ denote the group of $C^{\\infty}$ diffeomorphisms isotopic to the identity. We prove that any (discrete) group homomorphism between $\\text{Diff}_c(M)$ and $\\text{Diff}_c(N)$ is continuous. We also show that a non-trivial group homomorphism $\\Phi: \\text{Diff}_c(M) \\to \\text{Diff}_c(N)$ implies that $\\dim(M) \\leq \\dim(N)$ and give a classification of such homomorphisms when $\\dim(M) = \\dim(N)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4447","kind":"arxiv","version":4},"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"}