{"paper":{"title":"Examples of rational toral rank complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Toshihiro Yamaguchi","submitted_at":"2012-03-20T05:02:59Z","abstract_excerpt":"In \"A Hosse diagram for rational toral tanks,\" we see a CW complex ${\\mathcal T}(X)$, which gives a rational homotopical classification of almost free toral actions on spaces in the rational homotopy type of $X$ associated with rational toral ranks and also presents certain relations in them. We call it the {\\it rational toral rank complex} of $X$. It represents a variety of toral actions. In this note, we will give effective 2-dimensional examples of it when $X$ is a finite product of odd spheres. This is a combinatorial approach in rational homotopy theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4317","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"}