Notions of uniform manifolds

TL;DR

This paper introduces a definition of uniformity for noncompact manifolds that does not rely on Riemannian metrics, aligning with the concept of bounded geometry, and serves as a reference for ongoing research.

Contribution

It proposes a metric-independent notion of uniformity on noncompact manifolds, expanding the understanding of bounded geometry without Riemannian structures.

Findings

Defines a new concept of uniformity on manifolds

Shows equivalence to bounded geometry

Provides a reference for future research

Abstract

We explore a definition of uniformity on noncompact manifolds that does not require a Riemannian metric, but is equivalent to bounded gemetry. These are unfinished research notes (and will likely never be published), but since they were cited by other people, I'm submitting this here for easier referencing.