{"paper":{"title":"Topology and geometry of the canonical action of $T^4$ on the complex Grassmannian $G_{4,2}$ and the complex projective space $CP^{5}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.AT","authors_text":"Svjetlana Terzic, Victor M. Buchstaber","submitted_at":"2014-10-09T14:21:11Z","abstract_excerpt":"We consider the canonical action of the compact torus $T^4$ on the Grassmann manifold $G_{4,2}$ and prove that the orbit space $G_{4,2}/T^4$ is homeomorphic to the sphere $S^5$. We prove that the induced differentiable structure on $S^5$ is not the smooth one and describe the smooth and the singular points. We also consider the action of $T^4$ on $CP^5$ induced by the composition of the second symmetric power $T^4\\subset T^6$ and the standard action of $T^6$ on $CP^5$ and prove that the orbit space $CP^5/T^4$ is homeomorphic to the join $CP^2\\ast S^2$. The Pl\\\"ucker embedding $G_{4,2}\\subset C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2482","kind":"arxiv","version":3},"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"}