{"paper":{"title":"Homotopy Inertia Groups and Tangential Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ramesh Kasilingam","submitted_at":"2015-11-12T07:13:28Z","abstract_excerpt":"We show that if $M$ and $N$ have the same homotopy type of simply connected closed smooth $m$-manifolds such that the integral and mod-$2$ cohomologies of $M$ vanish in odd degrees, then their homotopy inertia groups are equal. Let $M^{2n}$ be a closed $(n-1)$-connected $2n$-dimensional smooth manifold. We show that, for $n=4$, the homotopy inertia group of $M^{2n}$ is trivial and if $n=8$ and $H^n(M^{2n};\\mathbb{Z})\\cong \\mathbb{Z}$, the homotopy inertia group of $M^{2n}$ is also trivial. We further compute the group $\\mathcal{C}(M^{2n})$ of concordance classes of smoothings of $M^{2n}$ for $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03802","kind":"arxiv","version":4},"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"}