{"paper":{"title":"The Swiss Cheese Theorem for Linear Operators with Two Invariant Subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Audrey Moore, Markus Schmidmeier","submitted_at":"2014-09-19T19:23:21Z","abstract_excerpt":"We study systems $(V,T,U_1,U_2)$ consisting of a finite dimensional vector space $V$, a nilpotent $k$-linear operator $T:V\\to V$ and two $T$-invariant subspaces $U_1\\subset U_2\\subset V$. Let $\\mathcal S(n)$ be the category of such systems where the operator $T$ acts with nilpotency index at most $n$. We determine the dimension types $(\\dim U_1, \\dim U_2/U_1, \\dim V/U_2)$ of indecomposable systems in $\\mathcal S(n)$ for $n\\leq 4$. It turns out that in the case where $n=4$ there are infinitely many such triples $(x,y,z)$, they all lie in the cylinder given by $|x-y|,|y-z|,|z-x|\\leq 4$. But not "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5772","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"}