{"paper":{"title":"A Homotopy-like Class Invariant for Sub-manifolds of Punctured Euclidean Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GT"],"primary_cat":"math.DG","authors_text":"Maxim Likhachev, Subhrajit Bhattacharya, Vijay Kumar","submitted_at":"2011-03-13T01:36:25Z","abstract_excerpt":"We consider the $D$-dimensional Euclidean space, $\\mathbb{R}^D$, with certain $(D-N)$-dimensional compact, closed and orientable sub-manifolds (which we call \\emph{singularity manifolds} and represent by $\\widetilde{\\mathcal{S}}$) removed from it. We define and investigate the problem of finding a homotopy-like class invariant ($\\chi$-homotopy) for certain $(N-1)$-dimensional compact, closed and orientable sub-manifolds (which we call \\emph{candidate manifolds} and represent by $\\omega$) of $\\mathbb{R}^D \\setminus \\widetilde{\\mathcal{S}}$, with special emphasis on computational aspects of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2488","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"}