{"paper":{"title":"A compactification of outer space which is an absolute retract","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Camille Horbez, Mladen Bestvina","submitted_at":"2015-12-09T15:17:20Z","abstract_excerpt":"We define a new compactification of outer space $CV_N$ (the \\emph{Pacman compactification}) which is an absolute retract, for which the boundary is a $Z$-set. The classical compactification $\\overline{CV_N}$ made of very small $F_N$-actions on $\\mathbb{R}$-trees, however, fails to be locally $4$-connected as soon as $N\\ge 4$. The Pacman compactification is a blow-up of $\\overline{CV_N}$, obtained by assigning an orientation to every arc with nontrivial stabilizer in the trees."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02893","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"}