{"paper":{"title":"Odd characteristic classes in entire cyclic homology and equivariant loop space homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.KT","authors_text":"Batu G\\\"uneysu, Sergio Cacciatori","submitted_at":"2018-05-18T21:33:05Z","abstract_excerpt":"Given a compact manifold $M$ and $g\\in C^{\\infty}(M,U(l;\\mathbb{C}))$ we construct a Chern character $\\mathrm{Ch}^-(g)$ which lives in the odd part of the equivariant (entire) cyclic Chen-normalized bar complex $\\underline{\\mathscr{C}}(\\Omega_{\\mathbb{T}}(M\\times \\mathbb{T}))$ of $M$, and which is mapped to the odd Bismut-Chern character under the equivariant Chen integral map. It is also shown that the assignment $g\\mapsto \\mathrm{Ch}^-(g)$ induces a well-defined group homomorphism from the $K^{-1}$ theory of $M$ to the odd homology group of $\\underline{\\mathscr{C}}(\\Omega_{\\mathbb{T}}(M\\time"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07449","kind":"arxiv","version":2},"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"}