{"paper":{"title":"Smooth moduli spaces of associative submanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Damien Gayet (ICJ)","submitted_at":"2010-11-08T09:57:29Z","abstract_excerpt":"Let $M^7$ be a smooth manifold equipped with a $G_2$-structure $\\phi$, and $Y^3$ be an closed compact $\\phi$-associative submanifold. In \\cite{McL}, R. McLean proved that the moduli space $\\bm_{Y,\\phi}$ of the $\\phi$-associative deformations of $Y$ has vanishing virtual dimension. In this paper, we perturb $\\phi$ into a $G_2$-structure $\\psi$ in order to ensure the smoothness of $\\bm_{Y,\\psi}$ near $Y$. If $Y$ is allowed to have a boundary moving in a fixed coassociative submanifold $X$, it was proved in \\cite{GaWi} that the moduli space $\\bm_{Y,X}$ of the associative deformations of $Y$ with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1744","kind":"arxiv","version":3},"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"}