{"paper":{"title":"Image nonconcordance of positive-genus $\\pi_1$-injective surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Weizhe Niu","submitted_at":"2026-06-28T00:21:24Z","abstract_excerpt":"We construct, for every $g\\ge2$, infinite families of homotopic smooth embeddings of a closed genus-$g$ surface whose images are pairwise not smoothly image-concordant, while each surface is $\\pi_1$-injective. The main closed examples lie in one-fold stabilizations of closed aspherical mapping tori with torsion-free fundamental group: after stabilization by $S^2\\times S^2$, the surfaces have a common framed dual sphere and the inclusion of each complement induces a $\\pi_1$-isomorphism. The image-nonconcordance already occurs before stabilization, in the underlying closed aspherical mapping tor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29122","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/2606.29122/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"}