Index formulae for mixed boundary conditions on manifolds with corners

Autor:	Bohlen, Karsten
Rok vydání:	2017
Předmět:	Mathematics - Analysis of PDEs Mathematics - Differential Geometry 19K56
Druh dokumentu:	Working Paper
Popis:	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. Comment: 22 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1704.00535 Zobrazit plný text záznamu View this record from Arxiv