{"paper":{"title":"Combinatorial formulas for products of Thom classes","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.SG","authors_text":"Catalin Zara, Victor Guillemin","submitted_at":"2000-07-26T17:55:35Z","abstract_excerpt":"Let G be a torus of dimension n > 1 and M a compact Hamiltonian G-manifold with $M^G$ finite. A circle, $S^1$, in G is generic if $M^G = M^{S^1}$. For such a circle the moment map associated with its action on M is a perfect Morse function. Let $\\{ W_p^+ ; p \\in M^G\\}$ be the Morse-Whitney stratification of M associated with this function, and let $\\tau_p^+$ be the equivariant Thom class dual to $W_p^+$. These classes form a basis of $H_G^*(M)$ as a module over $\\SS(\\fg^*)$ and, in particular, $$\\tau_p^+ \\tau_q^+ = \\sum c_{pq}^r \\tau_r^+$$ with $c_{pq}^r \\in \\SS(\\fg^*)$. For manifolds of GKM t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0007166","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0007166/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}