{"paper":{"title":"Path components of $\\mathrm{G}_2$-moduli spaces may be non-aspherical","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Diarmuid Crowley, Sebastian Goette, Thorsten Hertl","submitted_at":"2025-03-20T03:51:11Z","abstract_excerpt":"Starting from Joyce's generalised Kummer construction, we exhibit non-trivial families of $\\mathrm{G}_2$-manifolds over the two dimensional sphere by resolving singularities with a twisted family of Eguchi-Hanson spaces. We establish that the comparison map $\\mathcal{G}_2^{\\mathrm{tf}}(M) /\\!\\!/ \\mathrm{Diff}(M)_0 \\rightarrow \\mathcal{G}_2^{\\mathrm{tf}}(M) / \\mathrm{Diff}(M)_0$ is a fibration over each path components with Eilenberg Mac Lane spaces as fibres, which allows us to show that these families remain non-trivial in $\\mathcal{G}_2^{\\mathrm{tf}}(M) / \\mathrm{Diff}(M)_0$. In addition, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.15829","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.15829/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}