{"paper":{"title":"Some perspective on Homotopy obstructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Bibekananda Mishra, Satya Mandal","submitted_at":"2018-11-11T23:43:54Z","abstract_excerpt":"Throughout $A$ will denote commutative noetherian ring, with $\\dim A=d\\geq 2$, and $P$ denote a projective $A$-module with $rank(P)=n$. In \\cite{MM1} we considered the Homotopy obstruction sets $\\pi_0\\left({\\mathcal LO}(P)\\right)$, which has a structure of an abelian monoid, under suitable regularity and other conditions. In this article, we provide some perspective on these sets $\\pi_0\\left({\\mathcal LO}(P)\\right)$.\n  Under similar regularity and other conditions, we prove if $P, Q$ are two projective $A$-modules, with $rank(P)=rank(Q)=d$ and $\\det(P) \\cong \\det Q$, then $\\pi_0\\left({\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04510","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"}