{"paper":{"title":"Talbot Workshop 2010 Talk 2: K-Theory and Index Theory","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.KT","authors_text":"Chris Kottke","submitted_at":"2010-10-24T21:05:40Z","abstract_excerpt":"These are notes from a talk at the 2010 Talbot Workshop on Twisted K-theory and Loop Groups. This particular talk is an overview of index theory from the point of view of topological K-theory. Assuming little background in analysis, but some familiarity with complex K-theory, the talk covers the (families) Atiyah-Singer index theorem from the point of view of Gysin maps for fibrations, and orientations for complex K-theory in terms of spin^c structures, Clifford algebras and Dirac operators. Higher index theory is also discussed, in terms of Cl_k modules and Cl_k-linear operators. It is meant "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5002","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"}