{"paper":{"title":"On Lusternik-Schnirelmann category of SO(10)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Kai Kikuchi, Norio Iwase, Toshiyuki Miyauchi","submitted_at":"2007-12-21T07:56:11Z","abstract_excerpt":"Let $G$ be a compact connected Lie group and $p : E\\to \\Sigma A$ be a principal G-bundle with a characteristic map $\\alpha : A\\to G$, where $A=\\Sigma A_{0}$ for some $A_{0}$. Let $\\{K_{i}{\\to} F_{i-1}{\\hookrightarrow} F_{i} \\,|\\, 1{\\le} i {\\le} n,\\, F_{0}{=} \\{\\ast\\} \\; F_{1}{=} \\Sigma{K_{1}} \\; \\text{and}\\; F_{n}{\\simeq} G \\}$ be a cone-decomposition of $G$ of length $m$ and $F'_{1}=\\Sigma{K'_{1}} \\subset F_{1}$ with $K'_{1} \\subset K_{1}$ which satisfy $F_{i}F'_{1} \\subset F_{i+1}$ up to homotopy for any $i$. Our main result is as follows: we have $\\operatorname{cat}(X) \\le m{+}1$, if firstl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.3637","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"}