{"paper":{"title":"Maps between circle bundles: Fiber-preserving, Finiteness and Realization of mapping degree sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR","math.NT"],"primary_cat":"math.GT","authors_text":"Christoforos Neofytidis, Hongbin Sun, Shicheng Wang, Ye Tian, Zhongzi Wang","submitted_at":"2025-05-22T06:32:03Z","abstract_excerpt":"Let $E_i$ be an oriented circle bundle over a closed oriented aspherical $n$-manifold $M_i$ with Euler class $e_i\\in H^2(M_i;\\mathbb{Z})$, $i=1,2$. We prove the following:\n  (i) If every finite-index subgroup of $\\pi_1(M_2)$ has trivial center, then any non-zero degree map from $E_1$ to $E_2$ is homotopic to a fiber-preserving map.\n  (ii) The mapping degree set of fiber-preserving maps from $E_1$ to $E_2$ is given by $$\\{0\\} \\cup\\{k\\cdot \\mathrm{deg}(f) \\ | \\, k\\ne 0, \\ f\\colon M_1\\to M_2 \\, \\text{with} \\, \\mathrm{deg}(f)\\ne 0 \\ \\text{such that}\\, f^\\#(e_2)=ke_1\\},$$ where $f^\\# \\colon H^2(M_2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.16285","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/2505.16285/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"}