{"paper":{"title":"On $L_2$-cohomology of almost Hermitian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Adriano Tomassini, Richard Hind","submitted_at":"2017-08-21T16:42:24Z","abstract_excerpt":"Let $(X,J,\\omega,g)$ be a complete $n$-dimensional K\\\"ahler manifold. A Theorem by Gromov \\cite{G} states that the if the K\\\"ahler form is $d$-bounded, then the space of harmonic $L_2$ forms of degree $k$ is trivial, unless $k=\\frac{n}{2}$. Starting with a contact manifold $(M,\\alpha)$ we show that the same conclusion does not hold in the category of almost K\\\"ahler manifolds. Let $(X,J,g)$ be a complete almost Hermitian manifold of dimension four. We prove that the reduced $L_2$ $2^{nd}$-cohomology group decomposes as direct sum of the closure of the invariant and anti-invariant $L_2$-cohomol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06316","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"}