Abstract
We calculate the homotopy groups of the space of elliptic boundary value problems for an elliptic differential operatorA of a first order and of the space of elliptic self-adjoint boundary value problems whenA is a formally self-adjoint. In particular we show that the spectral flow of anS 1 family of self-adjoint elliptic boundary value problems is well defined. This provides some information on spectral properties along the lines of the Vafa-Witten approach to spectral inequalities.
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Communicated by A. Jaffe
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Booss-Bavnbek, B., Wojciechowski, K.P. Pseudo-differential projections and the topology of certain spaces of elliptic boundary value problems. Commun.Math. Phys. 121, 1–9 (1989). https://doi.org/10.1007/BF01218620
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DOI: https://doi.org/10.1007/BF01218620