{"paper":{"title":"Free ${\\Bbb Z}^p$-actions on the three dimensional torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eduardo Fierro Morales, Richard Urz\\'ua-Luz","submitted_at":"2019-06-27T06:08:56Z","abstract_excerpt":"We show that for each natural $p\\geq 2$, the Lefschetz fixed point theorem is optimal when applied to ${\\Bbb Z}^{p}$-actions by homeomorphisms on the three dimensional torus ${\\Bbb T}^3$. More precisely, we show that for a spectrally unitary ${\\Bbb Z}^p$-action ${\\bf A}$ on the first homology group $H_1({\\Bbb T}^3,{\\Bbb Z})$ with trivial fixed point set, there exists a free ${\\Bbb Z}^p$-action by real analytic diffeomorphisms of ${\\Bbb T}^3$ whose induced ${\\Bbb Z}^p$-action on $H_1({\\Bbb T}^3,{\\Bbb Z})$ is the action ${\\bf A}$. In particular, we establish the normal form for this type of acti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11448","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"}