# Stratified Whitehead's theorem and knot invariants

## TL;DR

This paper introduces stratified homotopy groups as invariants for stratified spaces, establishes a stratified version of Whitehead's theorem, and applies these concepts to define a complete knot invariant.

## Contribution

It develops stratified homotopy groups and proves a stratified Whitehead theorem, providing new tools for classifying stratified spaces and knots.

## Key findings

- Stratified homotopy groups satisfy a stratified Whitehead theorem.
- A complete knot invariant is constructed using stratified homotopy groups.
- The approach links stratified topology with knot theory.

## Abstract

By considering homotopies that preserve the stratification, one obtains a natural notion of homotopy for stratified spaces. In this short note, we introduce invariants of stratified homotopy, the stratified homotopy groups. We show that they satisify a stratified version of Whitehead's theorem. As an example, we introduce a complete knot invariant defined via the stratified homotopy groups ----- En consid\'erant des homotopies pr\'eservant la stratification, on obtient une notion naturelle d'homotopie pour les espaces stratifi\'es. Dans cette note, on pr\'esente des invariants d'homotopie stratifi\'ee, les groupes d'homotopie stratifi\'es. On montre que ces groupes d'homotopie stratifi\'es v\'erifient un analogue stratifi\'e au th\'eor\`eme de Whitehead. Comme illustration, on pr\'esente un invariant de noeud complet d\'efini \`a partir des groupes d'homotopie stratifi\'es.