{"paper":{"title":"Quantum characteristic classes and the Hofer metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Yasha Savelyev","submitted_at":"2007-09-27T23:30:51Z","abstract_excerpt":"Given a closed monotone symplectic manifold $M$, we define certain characteristic cohomology classes of the free loop space $L \\text {Ham}(M, \\omega)$ with values in $QH_* (M)$, and their $S^1$ equivariant version. These classes generalize the Seidel representation and satisfy versions of the axioms for Chern classes. In particular there is a Whitney sum formula, which gives rise to a graded ring homomorphism from the ring $H_{*} (L\\text {Ham}(M, \\omega), \\mathbb{Q})$, with its Pontryagin product to $QH_{2n+*} (M)$ with its quantum product. As an application we prove an extension of a theorem "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.4510","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":""},"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"}