{"paper":{"title":"Cohomological estimates for $\\cat(X,\\xi)$","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dirk Schuetz, Michael Farber","submitted_at":"2006-08-31T21:41:25Z","abstract_excerpt":"This paper studies the homotopy invariant $\\cat(X,\\xi)$ introduced in \\cite{farbe2}. Given a finite cell-complex $X$, we study the function $\\xi\\mapsto \\cat(X,\\xi)$ where $\\xi$ varies in the cohomology space $H^1(X;\\R)$. Note that $\\cat(X,\\xi)$ turns into the classical Lusternik - Schnirelmann category $\\cat(X)$ in the case $\\xi=0$. Interest in $\\cat(X,\\xi)$ is based on its applications in dynamics where it enters estimates of complexity of the chain recurrent set of a flow admitting Lyapunov closed 1-forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609005","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"}