{"paper":{"title":"Immersions of surfaces in spin$^c$-manifolds with Higgs fields","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrzej Derdzinski (Ohio State University, Columbus, Ohio, Poland), Tadeusz Januszkiewicz (Wroclaw University, USA), Wroclaw","submitted_at":"2002-10-16T21:01:03Z","abstract_excerpt":"We define a `Higgs field' for a four-dimensional spin$^c$-manifold to be a smooth section of its positive half-spinor bundle, transverse to the zero section, and defined only up to a positive functional factor. This is intended to be a generalization of almost complex structures on real four-manifolds, each of which may in fact be treated as a Higgs field without zeros for a specific spin$^c$-structure. The notions of totally real or pseudoholomorphic immersions of real surfaces in an almost complex manifold of real dimension four have straighforward generalizations to the case of a spin$^c$-m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0210253","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":""},"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"}