Injectivity radius of manifolds with a Lie structure at infinity

TL;DR

This paper proves that manifolds with a Lie structure at infinity have a positive injectivity radius using Lie groupoids, ensuring certain geometric regularities at infinity.

Contribution

It introduces a novel approach employing Lie groupoids to establish positivity of the injectivity radius for manifolds with a Lie structure at infinity.

Findings

Injectivity radius is positive for these manifolds.

Lie groupoids are effective tools for geometric analysis.

Provides a new perspective on the geometry at infinity.

Abstract

Using Lie groupoids, we prove that the injectivity radius of a manifold with a Lie structure at infinity is positive.