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On a spectral flow of Fredholm operators

Le : 20/04/2010 13h15
Par : Marina PROKHOROVA (MPIM Bonn et l'Institut de Mathematiques Acad. Sci. Rus., Ekaterinbourg)
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Résumé : The spectral flow of 1-parameter family of self-adjoint Fredholm operators is the algebraic number of operator's eigenvaluesintersecting 0. Let X be a compact surface, E be a complex vector bundle over X. The main goal of this talk is the computation of the spectral flow along any 1-parameter family (A_t, B_t) such that A_t is 1st order self-adjoint elliptic operators on E, B_t is self-adjoint elliptic local boundary conditions for A_t, and (A_1, B_1) is obtained from(A_0, B_0) by some unitary isomorphism of E.