{"paper":{"title":"Higher-degree bounded cohomology of transformation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Martin Nitsche","submitted_at":"2021-05-18T17:33:56Z","abstract_excerpt":"For $M$ a compact Riemannian manifold Brandenbursky and Marcinkowski constructed a transfer map $H_b^*(\\pi_1(M))\\to H_b^*(Homeo_{vol,0}(M))$ and used it to show that for certain $M$ the space $\\overline{EH}_b^3(Homeo_{vol,0}(M))$ is infinite-dimensional. Kimura adapted the argument to $Diff_{vol}(D^2,\\partial D^2)$. We extend both results to the higher degrees $\\overline{EH}_b^{2n}$, $n\\geq 1$. We also show that for certain $M$ the ordinary cohomology $H^*(Homeo_{vol,0}(M))$ is non-trivial in all degrees. In our computations we view the transfer map as being induced by a coupling of groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.08698","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.08698/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}