Regular Homotopy

(Differential Topology)

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Differential Topology
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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


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