{"paper":{"title":"Free and semi-inert cell attachments","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Peter Bubenik","submitted_at":"2003-12-19T17:48:08Z","abstract_excerpt":"Let $Y$ be the space obtained by attaching a finite-type wedge of cells to a simply-connected, finite-type CW-complex.\n  We introduce the free and semi-inert conditions on the attaching map which broadly generalize the previously studied inert condition. Under these conditions we determine $H_*(\\Omega Y;R)$ as an $R$-module and as an $R$-algebra respectively. Under a further condition we show that $H_*(\\Omega Y;R)$ is generated by Hurewicz images.\n  As an example we study an infinite family of spaces constructed using only semi-inert cell attachments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0312387","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"}