{"paper":{"title":"Bifurcation of Fredholm Maps I; The Index Bundle and Bifurcation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.AT"],"primary_cat":"math.DG","authors_text":"Jacobo Pejsachowicz","submitted_at":"2010-05-07T08:44:17Z","abstract_excerpt":"We associate to a parametrized family $f$ of nonlinear Fredholm maps possessing a trivial branch of zeroes an {\\it index of bifurcation} $\\beta(f)$ which provides an algebraic measure for the number of bifurcation points from the trivial branch. The index $\\beta(f)$ is derived from the index bundle of the linearization of the family along the trivial branch by means of the generalized $J$-homomorphism. Using the Agranovich reduction and a cohomological form of the Atiyah-Singer family index theorem, due to Fedosov, we compute the bifurcation index of a multiparameter family of nonlinear ellipt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2077","kind":"arxiv","version":5},"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"}