Simple Homotopy Equivalence of Nearby Lagrangians

TL;DR

This paper proves that for a closed exact Lagrangian in a cotangent bundle, the projection to the base manifold is a simple homotopy equivalence, linking symplectic geometry with algebraic topology.

Contribution

It establishes a new topological property of Lagrangians in cotangent bundles, showing the projection map is a simple homotopy equivalence.

Findings

Projection to the base is a simple homotopy equivalence for closed exact Lagrangians.

Connects symplectic geometry with algebraic topology.

Provides a new topological insight into Lagrangian submanifolds.

Abstract

Given a closed exact Lagrangian in the cotangent bundle of a closed smooth manifold, we prove that the projection to the base is a simple homotopy equivalence.