{"paper":{"title":"Higher Spectral Flow for Dirac Operators with Local Boundary Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jianqing Yu","submitted_at":"2014-10-22T10:56:33Z","abstract_excerpt":"We consider a gauge invariant one parameter family of families of fiberwise twisted Dirac type operators on a fiberation with the typical fiber an even dimensional compact manifold with boundary, i.e., a family $\\{D_u\\}, u\\in [0,1]$ with $D_1=gD_0g^{-1}$ for a suitable unitary automorphism $g$ of the twisted bundle. Suppose all the operators $D_u$ are imposed with a certain \\emph{local elliptic} boundary condition $F$ and $D_{u,F}$ is the self-adjoint extension of $D_u$. We establish a formula for the higher spectral flow of $\\{D_{u,F}\\}$, $u\\in[0,1]$. Our result generalizes a recent result of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5988","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"}