1998/12/21 by Simon Scott, Scott, Simon
Mathematics · #11S45 #58G20 #58G26 #Advanced Operator Algebra Research #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #math.AP #math.DG #msc:11S45 #msc:58G20 #msc:58G26
paper · pdf · doi:10.48550/arxiv.math/9812124
To appear in Proc. Am. Math. Soc
arxiv created 1998/12/21 · openalex publication_date 1998/12/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with contributions from the families of Dirac operators over the two halves. This curvature form is the natural differential representative which satisifies the same splitting principle as the Chern class of the determinant line bundle.