{"paper":{"title":"Stability for boundary actions of cocompact lattices in Euclidean buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.MG"],"primary_cat":"math.DS","authors_text":"Thang Nguyen, Theodore Weisman","submitted_at":"2026-07-16T07:35:21Z","abstract_excerpt":"When $X$ is a locally compact Euclidean building, the isometry group\n  of $X$ acts by homeomorphisms on the space of $k$-simplices in the\n  visual boundary of $X$. We consider perturbations of these actions\n  for discrete groups of isometries acting with compact quotient on\n  $X$, showing that all small enough perturbations are semi-conjugate\n  to the original action. This proves in particular that, when $Q$ is\n  any parabolic subgroup in a semisimple $p$-adic Lie group $G$, the\n  induced action of a cocompact lattice in $G$ has a topologically\n  stable action on $G/Q$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14668","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.14668/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}