{"paper":{"title":"The monodromy theorem for compact K\\\"ahler manifolds and smooth quasi-projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Botong Wang, Nero Budur, Yongqiang Liu","submitted_at":"2016-09-21T09:36:53Z","abstract_excerpt":"Given any connected topological space $X$, assume that there exists an epimorphism $\\phi: \\pi_1(X) \\to \\mathbb{Z}$. The deck transformation group $\\mathbb{Z}$ acts on the associated infinite cyclic cover $X^\\phi$ of $X$, hence on the homology group $H_i(X^\\phi, \\mathbb{C})$. This action induces a linear automorphism on the torsion part of the homology group as a module over the Laurent ring $\\mathbb{C}[t,t^{-1}]$, which is a finite dimensional $\\mathbb{C}$-vector space. We study the sizes of the Jordan blocks of this linear automorphism. When $X$ is a compact K\\\"ahler manifold, we show that al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06478","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"}