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

Abstract

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 $L_0$. In particular, we consider the neighborhoods in this manifold of Lagrangians which intersect $L_0$ nontrivially.