The Dirichlet to Neumann operator for elliptic complexes

Tarkhanov, N.

doi:10.1090/S0002-9947-2011-05460-7

The Dirichlet to Neumann operator for elliptic complexes
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Trans. Amer. Math. Soc. 363 (2011), 6421-6437 Request permission

Abstract:

We define the Dirichlet to Neumann operator for an elliptic complex of first order differential operators on a compact Riemannian manifold with boundary. Under reasonable conditions the Betti numbers of the complex prove to be completely determined by the Dirichlet to Neumann operator on the boundary.

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