Local systems and vanishing Maslov class

TL;DR

This paper simplifies the proof that closed exact Lagrangians in cotangent bundles have vanishing Maslov class and extends the result to a broader class of Weinstein domains.

Contribution

It provides a streamlined proof of the vanishing Maslov class and generalizes it to a wider class of Weinstein domains.

Findings

Simplified proof of vanishing Maslov class for closed exact Lagrangians.

Extended the vanishing Maslov class result to more Weinstein domains.

Confirmed homotopy equivalence to the zero section for these Lagrangians.

Abstract

It is well known that closed exact Lagrangians in cotangent bundles of closed manifolds have vanishing Maslov class and are homotopy equivalent to the zero section. In this paper we greatly simplify the proof of vanishing Maslov class and generalize the proof to a slightly larger family of Weinstein domains.