{"paper":{"title":"Assignments for topological group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AT","authors_text":"Augustin-Liviu Mare, Oliver Goertsches","submitted_at":"2015-12-21T11:03:01Z","abstract_excerpt":"A polynomial assignment for a continuous action of a compact torus $T$ on a topological space $X$ assigns to each $p\\in X$ a polynomial function on the Lie algebra of the isotropy group at $p$ in such a way that a certain compatibility condition is satisfied. The space ${\\mathcal{A}}_T(X)$ of all polynomial assignments has a natural structure of an algebra over the polynomial ring of ${\\rm Lie}(T)$. It is an equivariant homotopy invariant, canonically related to the equivariant cohomology algebra. In this paper we prove various properties of ${\\mathcal{A}}_T(X)$ such as Borel localization, a C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06579","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"}