{"paper":{"title":"A Geometric Realization of Spherical T-Duality via $\\star$-Diagrams","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.SG"],"primary_cat":"math.DG","authors_text":"Leonardo F. Cavenaghi, Lino Grama, Ludmil Katzarkov","submitted_at":"2024-04-29T20:00:42Z","abstract_excerpt":"We relate spherical T-duality for oriented linear $\\mathrm{S}^3$-bundles over $\\mathrm{S}^4$ (the Milnor bundles $M_{m,n}$, which are $\\mathrm{S}^3$-principal exactly when $m=0$ or $n=0$, and whose total spaces are homotopy $7$-spheres exactly when $m+n=\\pm1$) to $\\star$-diagrams and to a higher-dimensional generalization of the logarithmic transformations of $4$-manifold topology.\n  For an $\\mathrm{S}^3$-principal pair $(P,H)$, $(\\widehat P,\\widehat H)$ over $\\mathrm{S}^4$, we show that the T-duality correspondence space $P\\times_{\\mathrm{S}^4}\\widehat P$ is itself a $\\star$-diagram of a dist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.19088","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.19088/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"}