{"paper":{"title":"On Euler characteristic and fundamental groups of compact manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bing-Long Chen, Xiaokui Yang","submitted_at":"2017-11-09T10:12:54Z","abstract_excerpt":"Let $M$ be a compact Riemannian manifold, $\\pi:\\widetilde{M}\\rightarrow M$ be the universal covering and $\\omega$ be a smooth $2$-form on $M$ with $\\pi^*\\omega$ cohomologous to zero. Suppose the fundamental group $\\pi_1(M)$ satisfies certain radial quadratic (resp. linear) isoperimetric inequality, we show that there exists a smooth $1$-form $\\eta$ on $\\widetilde M$ of linear (resp. bounded) growth such that $\\pi^*\\omega=d \\eta$. As applications, we prove that on a compact Kahler manifold $(M,\\omega)$ with $\\pi^*\\omega$ cohomologous to zero, if $\\pi_1(M)$ is $\\mathrm{CAT}(0)$ or automatic (res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03309","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"}