{"paper":{"title":"Fibrewise Orbifold Resolutions with Applications to $\\mathrm{G}_2$-Moduli Spaces","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.AT","authors_text":"Thorsten Hertl","submitted_at":"2026-06-19T06:08:03Z","abstract_excerpt":"By resolving the singularities of tailor-made orbifolds via twisted families of blow-ups, we construct manifold bundles $M \\rightarrow E \\rightarrow S^2$. Using tools from real homotopy theory, we show that these bundles determine a free subgroup in $\\pi_2(B\\mathrm{hAut}(M)_0)$. The proof relies on a generalisation of Sullivan's result, which describes the real homotopy groups of the monoid of homotopy automorphisms $\\mathrm{hAut}(X)$ in terms of derivations of the minimal model of $X$, to the monoid $\\mathrm{hAut}_A(X)$ of relative homotopy automorphisms.\n  As an application, we prove that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21128","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/2606.21128/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"}