Index formulae for mixed boundary conditions on manifolds with corners

Karsten Bohlen

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arXiv · 1704.00535

Index formulae for mixed boundary conditions on manifolds with corners

Karsten Bohlen

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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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Karsten Bohlen. 2017-04-08. Index formulae for mixed boundary conditions on manifolds with corners. https://arxiv.org/abs/1704.00535

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