# Regular Homotopy

## What is Regular homotopy?

In the mathematical field of topology, a regular homotopy refers to a special kind of homotopy between immersions of one manifold in another. The homotopy must be a 1-parameter family of immersions. Similar to homotopy classes, one defines two immersions to be in the same regular homotopy class if there exists a regular homotopy between them. Regular homotopy for immersions is similar to isotopy of embeddings: they are both restricted types of homotopies. Stated another way, two continuous functions are homotopic if they represent points in the same path-components of the mapping space , given the compact-open topology. The space of immersions is the subspace of consisting of immersions, denote it by . Two immersions are regularly homotopic if they represent points in the same path-component of .

### Technology Types

algebraic topologydifferential topology

### Synonyms

Whitney-Graustein theoremWhitney–Graustein theorem

### Translations

Satz von Whitney-Graustein (de)

## Tech Info

Source: [object Object]
— Date merged: 11/6/2021, 1:32:52 PM
— Date scraped: 5/20/2021, 5:53:17 PM