{"paper":{"title":"Flat connections and cohomology invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Indranil Biswas, Marco Castrill\\'on L\\'opez","submitted_at":"2017-04-18T16:35:49Z","abstract_excerpt":"The main goal of this article is to construct some geometric invariants for the topology of the set $\\mathcal{F}$ of flat connections on a principal $G$-bundle $P\\,\\longrightarrow\\, M$. Although the characteristic classes of principal bundles are trivial when $\\mathcal{F}\\neq \\emptyset$, their classical Chern-Weil construction can still be exploited to define a homomorphism from the set of homology classes of maps $S\\longrightarrow \\mathcal{F}$ to the cohomology group $H^{2r-k}(M,\\mathbb{R})$, where $S$ is null-cobordant $(k-1)$-manifold, once a $G$-invariant polynomial $p$ of degree $r$ on $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05414","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"}