Arcs, Cords and Felts - Six instances of the Linearization Principle

TL;DR

This paper demonstrates how key results in singularity theory and differential geometry can be derived from a single foundational theorem, the Rank Theorem for maps between power series spaces.

Contribution

It introduces a unifying approach that simplifies the derivation of multiple important results using the Rank Theorem.

Findings

Key results in singularity theory are deduced from the Rank Theorem.

Key results in differential geometry are deduced from the Rank Theorem.

The approach provides a unified framework for understanding these results.

Abstract

It is shown how a selection of prominent results in singularity theory and differential geometry can be deduced from one theorem, the Rank Theorem for maps between spaces of power series.