  Let {D_x} be a family of unbounded self-adjoint Fredholm operators
representing an element of K^1(M). Consider the first two components of the
Chern character of the family. It is known that these correspond to the
spectral flow of the family and the index gerbe. In this paper we consider
descriptions of these classes, both of which are in the spirit of holonomy.
These are then studied for families parametrized by a closed 3-manifold. A
connection between the multiplicity of the spectrum (and how it varies) and
these classes is developed.
