{"paper":{"title":"Homologies of inverse limits of groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Danil Akhtiamov","submitted_at":"2018-12-20T13:48:27Z","abstract_excerpt":"Let $H_n$ be the $n$-th group homology functor (with integer coeffcients) and let $\\{G_i\\} _ {i \\in \\mathbb{N}}$ be any tower of groups such that all maps $G_{i+1} \\to G_i$ are surjective. In this work we study kernel and cokernel of the following natural map: $$H_n(\\varprojlim G_i) \\to \\varprojlim H_n(G_i)$$ For $n=1$ Barnea and Shelah [BS] proved that this map is surjective and its kernel is a cotorsion group for any such tower $\\{G_i\\} _ {i \\in \\mathbb{N}}$. We show that for $n=2$ the kernel can be non-cotorsion group even in the case when all $G_i$ are abelian and after it we study these k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01125","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"}