THE ETA-FORM AND A GENERALIZED MASLOV INDEX

Given a family {L-0(b), L-1(b)}(b is an element of B) Of pairs of tran sverse Lagrangian subspaces of a hermitean symplectic vector space we define a family of Dirac operators on the unit interval and consider i ts eta-form eta(L-0, L-1) is an element of Omega (B). To a family {L- 0(b), L-1(b); L-2(b)}(b is an element of B) of pairwise transverse Lag rangian subspaces we associate the cocycle eta(L-0, L-1) + eta(L-1, L- 2) + eta(L-2, L-1) which is a closed form. We identify its cohomology class with a generalization to families of the triple Maslov index.