Index formulae for mixed boundary conditions on manifolds with corners

2017/04/03 by Karsten Bohlen, Bohlen, Karsten
Mathematics · #19K56 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1704.00535

openalex publication_date 2017/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the problem of calculating the Fredholm index of a geometric Dirac operator subject to local (e.g. Dirichlet and Neumann) and non-local (APS) boundary conditions posed on the strata of a manifold with corners. The boundary strata of the manifold with corners can intersect in higher codimension. To calculate the index we introduce a glueing construction and a corresponding Lie groupoid. We describe the Dirac operator subject to mixed boundary conditions via an equivariant family of Dirac operators on the fibers of the Lie groupoid. Using a heat kernel method with rescaling we derive a general index formula of the Atiyah-Singer type.

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