{"paper":{"title":"Generalized string topology operations","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Kate Gruher, Paolo Salvatore","submitted_at":"2006-02-10T10:15:55Z","abstract_excerpt":"We show that the Chas-Sullivan loop product, a combination of the Pontrjagin product on the fiber and intersection product on the base, makes sense on the total space homology of any fiberwise monoid E over a closed oriented manifold M. More generally the Thom spectrum E^{-TM} is a ring spectrum. Similarly a fiberwise module over E defines a module over E^{-TM}. Fiberwise monoids include adjoint bundles of principal bundles, and the construction is natural with respect to maps of principal bundles. This naturality implies homotopy invariance of the algebra structure on H_*(LM) arising from the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602210","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"}