Maslov Indicies In Symplectic Geometry Revisited

Thirty years ago in ``On the Maslov Index’’ the present authors with their late collaborator Prof. Ronnie Lee of Yale University presented an axiomatization of the Maslov index, an integer-valued invariant of continuous, piecewise smooth paths of pairs of Lagrangians. Four distinct methods of definition of such Maslov indicies were given; each satisfying the axioms. Here two more are offered and comparisons are made to the recent work of Her and Zhong defining an invariant of a path of symplectic matrices motivated by earlier work of Lidskii and Gelfand, Salomon and Zehnder.