{"paper":{"title":"Derivatives of embedding functors I: the stable case","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Gregory Arone","submitted_at":"2007-07-24T08:09:05Z","abstract_excerpt":"For smooth manifolds $M$ and $N$, let $\\Ebar(M, N)$ be the homotopy fiber of the map $\\Emb(M, N)\\longrightarrow \\Imm(M, N)$. Consider the functor from the category of Euclidean spaces to the category of spectra, defined by the formula $V\\mapsto \\Sigma^\\infty\\Ebar(M, N\\times V)$. In this paper, we describe the Taylor polynomials of this functor, in the sense of M. Weiss' orthogonal calculus, in the case when $N$ is a nice open submanifold of a Euclidean space. This leads to a description of the derivatives of this functor when $N$ is a tame stably parallelizable manifold (we believe that the pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3489","kind":"arxiv","version":2},"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"}