{"paper":{"title":"Obstructions to representations up to homotopy and ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Madeleine Jotz Lean","submitted_at":"2019-05-24T13:50:13Z","abstract_excerpt":"This paper considers the Pontryagin characters of graded vector bundles of finite rank, in the cohomology vector spaces of a Lie algebroid over the same base. These Pontryagin characters vanish if the graded vector bundle carries a representation up to homotopy of the Lie algebroid. As a consequence, this gives a strong obstruction to the existence of a representation up to homotopy on a graded vector bundle of finite rank. In particular, if a graded vector bundle $E[0]\\oplus F[1]\\to M$ carries a $2$-term representation up to homotopy of a Lie algebroid $A\\to M$, then all the (classical) $A$-P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10237","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"}