{"paper":{"title":"Constructing the virtual fundamental class of a Kuranishi atlas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.SG","authors_text":"Dusa McDuff","submitted_at":"2017-08-03T13:26:09Z","abstract_excerpt":"Consider a space $X$, such as a compact space of $J$-holomorphic stable maps, that is the zero set of a Kuranishi atlas. This note explains how to define the virtual fundamental class of $X$ by representing $X$ via the zero set of a map $S_M: M\\to E$, where $E$ is a finite dimensional vector space and the domain $M$ is an oriented, weighted branched topological manifold. Moreover, $S_M$ is equivariant under the action of the global isotropy group $\\Gamma$ on $M$ and $E$. This tuple $(M,E, \\Gamma, S_M)$ together with a homeomorphism $S_M^{-1}(0)/\\Gamma \\to X$ forms a single finite dimensional m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01127","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"}