{"paper":{"title":"Deformations of associative submanifolds with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Damien Gayet, Frederik Witt","submitted_at":"2008-02-09T19:48:51Z","abstract_excerpt":"Let $M$ be a topological $G_2$-manifold. We prove that the space of infinitesimal associative deformations of a compact associative submanifold $Y$ with boundary in a coassociative submanifold $X$ is the solution space of an elliptic problem. For a connected boundary $\\partial Y$ of genus $g$, the index is given by $\\int_{\\partial Y}c_1(\\nu_X)+1-g$, where $\\nu_X$ denotes the orthogonal complement of $T\\partial Y$ in $TX_{|\\partial Y}$ and $c_1(\\nu_X)$ the first Chern class of $\\nu_X$ with respect to its natural complex structure. Further, we exhibit explicit examples of non-trivial index."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.1283","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"}