Maslov index formulas for Whitney n-gons

TL;DR

This paper derives explicit formulas for the Maslov index of Whitney n-gons and their intersection numbers in the symmetric product of a surface, aiding in the understanding of their geometric properties.

Contribution

It provides new explicit formulas for Maslov indices and intersection numbers of Whitney n-gons in symmetric products, advancing computational techniques in symplectic geometry.

Findings

Explicit Maslov index formula for Whitney n-gons

Intersection number formula with the fat diagonal

Simplifies calculations in symplectic topology

Abstract

In this short article, we find an explicit formula for Maslov index of Whitney n-gons joining intersections points of n half-dimensional tori in the symmetric product of a surface. The method also yields a formula for the intersection number of such an n-gon with the fat diagonal in the symmetric product.