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In this paper we extend a theorem of Nicolaescu on spectral flow and the Maslov index. We do this by studying the manifold of Lagrangian subspaces of a symplectic Hilbert space that are Fredholm with respect to a given Lagrangian Lo. In particular, we consider the neighborhoods in this manifold of Lagrangians which intersect Lo nontrivially.

An extension of a theorem of Nicolaescu on spectral flow and the Maslov index