A Maslov-Type Index in Dimension 2

Abstract

In this article, we define an index of the Maslov type for paths of 2×2 orthogonal symplectic matrices. The starting point is an arbitrary 2×2 orthogonal symplectic matrix rather than the identity matrix. We use this index to explain the geometric intersection number of a pair of Lagrangian paths and compare it with the Cappell–Lee–Miller index.

Keywords

• Maslov index
• symplectic path
• Lagrangian path