Higher Spectral Flow for Dirac Operators with Local Boundary Conditions

2014/10/22 by Jianqing Yu, Yu, Jianqing
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.DG

paper · pdf · doi:10.48550/arxiv.1410.5988

arxiv created 2014/10/22 · openalex publication_date 2014/10/22 · arxiv updated 2014/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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∈ [0,1] with D₁=gD₀g^-1 for a suitable unitary automorphism g of the twisted bundle. Suppose all the operators D_u are imposed with a certain 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∈[0,1]. Our result generalizes a recent result of Gorokhovsky and Lesch to the families case.

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