Abstract
We give a simplified proof of the Yoshida–Nicolaescu Theorem in the product case using the theory of partial signatures as in Giambò et al. (2004). The theorem gives the equality of the spectral flow of a family of first order self-adjoint differential operators defined on sections of a Hermitian vector bundle over a partitioned manifold and the Maslov index of the corresponding pair of Cauchy data spaces. No nondegeneracy assumption is made on the endpoints of the path of differential operators.
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Research supported by Fapesp, São Paulo, Brasil, grants 01/00046-3, 04/14323-7 and 02/02528-8. The second author is partially sponsored by Cnpq, Brasil.
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Eidam, J.C.C., Piccione, P. A generalization of Yoshida–Nicolaescu theorem using partial signatures. Math. Z. 255, 357–372 (2007). https://doi.org/10.1007/s00209-006-0029-8
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DOI: https://doi.org/10.1007/s00209-006-0029-8