Order of tangency between manifolds

TL;DR

This paper investigates the concept of tangency order between manifolds of the same dimension, providing multiple geometric interpretations and discussing related concepts like regular separation exponents.

Contribution

It introduces a new understanding of tangency order with three distinct geometric interpretations and explores related concepts such as regular separation exponents.

Findings

Three different geometric interpretations of tangency order

Connections between tangency order and regular separation exponents

Insights into the geometric structure of manifold intersections

Abstract

We study the order of tangency between two manifolds of same dimension and give that notion three quite different geometric interpretations. Related aspects of the order of tangency, e.g., regular separation exponents, are also discussed.