{"paper":{"title":"Thom isomorphism and Push-forward map in twisted K-theory","license":"","headline":"","cross_cats":["hep-th","math.DG"],"primary_cat":"math.KT","authors_text":"Alan L. Carey, Bai-Ling Wang","submitted_at":"2005-07-21T04:36:49Z","abstract_excerpt":"We establish the Thom isomorphism in twisted K-theory for any real vector bundle and develop the push-forward map in twisted K-theory for any differentiable proper map $f: X\\to Y$ (not necessarily K-oriented). The push-forward map generalizes the push-forward map in ordinary K-theory for any $K$-oriented differentiable proper map and the Atiyah-Singer index theorem of Dirac operators on Clifford modules. For $D$-branes satisfying Freed-Witten's anomaly cancellation condition in a manifold with a non-trivial $B$-field, we associate a canonical element in the twisted K-group to get the so-called"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0507414","kind":"arxiv","version":4},"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/0507414/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"}