{"paper":{"title":"Finiteness and infiniteness results for Torelli groups of (hyper-)K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT"],"primary_cat":"math.GT","authors_text":"Matthias Kreck, Yang Su","submitted_at":"2019-07-12T12:19:40Z","abstract_excerpt":"The Torelli group $\\mathcal T(X)$ of a closed smooth manifold $X$ is the subgroup of the mapping class group $\\pi_0(\\mathrm{Diff}^+(X))$ consisting of elements which act trivially on the integral cohomology of $X$. In this note we give counterexamples to Theorem 3.4 of Verbitsky's paper \"Mapping class group and a global Torelli theorem for hyperk\\\"ahler manifolds\" (Duke Math.~J.~162 (2013), no.~15, 2929-2986) which states that the Torelli group of simply connected K\\\"ahler manifolds of complex dimension $\\ge 3$ is finite. This is done by constructing under some mild conditions homomorphisms $J"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05693","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"}