{"paper":{"title":"Spectral Sequences in String Topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Lennart Meier","submitted_at":"2010-01-27T15:53:48Z","abstract_excerpt":"In this paper, we investigate the behaviour of the Serre spectral sequence with respect to the algebraic structures of string topology in generalized homology theories, specificially with the Chas-Sullivan product and the corresponding coproduct and module structures. We prove compatibility for two kinds of fibre bundles: the fibre bundle $\\Omega^n M \\to L^n M \\to M$ for an $h_*$-oriented manifold $M$ and the looped fibre bundle $L^n F \\to L^n E \\to L^n B$ of a fibre bunde $F \\to E \\to B$ of $h_*$-oriented manifolds. Our method lies in the construction of Gysin morphisms of spectral sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4906","kind":"arxiv","version":3},"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"}