{"paper":{"title":"The topology of nilpotent representations in reductive groups and their maximal compact subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT","math.GT","math.RT"],"primary_cat":"math.GR","authors_text":"Maxime Bergeron","submitted_at":"2013-10-18T17:51:05Z","abstract_excerpt":"Let G be a complex reductive linear algebraic group and let K be a maximal compact subgroup of G. Given a nilpotent group \\Gamma generated by r elements, we consider the representation spaces Hom(\\Gamma,G) and Hom(\\Gamma,K) with the natural topology induced from an embedding into G^r and K^r respectively. The goal of this paper is to prove that there is a strong deformation retraction of Hom(\\Gamma,G) onto Hom(\\Gamma,K). We also obtain a strong deformation retraction of the geometric invariant theory quotient Hom(\\Gamma,G)//G onto Hom(\\Gamma,K)/K."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5109","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"}