Skip to main content
homotopy

homotopy

1 9.9
A way to change one shape into another by bending it without cutting or gluing
  • noun
  • /ˈhoʊməˌtoʊpi/
  • Specialized
: homotopía
  • His research focuses on homotopy theory, in particular the unstable homotopy theory of Lie groups and related objects.

Examples

  • His research focuses on homotopy theory, in particular the unstable homotopy theory of Lie groups and related objects.

    Blog text (25)
  • So homotopy type theory has been suggested as a new foundation of mathematics.

  • As for homotopy type theory, I don't know enough about that.

  • posted by homotopy at 1:46 PM on March 6

    Blog text (11)
  • Posted by homotopy at 1:53 PM on March 6.

    Blog text (11)
  • In topology, a homotopy describes a continuous transformation from one geometric shape to another.

  • Studying homotopy allows mathematicians to understand how different shapes can be related through continuous deformations.

  • The concept of homotopy is essential in understanding the properties of spaces in algebraic topology.

Synonyms

isotopy
vshomotopy
  • Specialized
9.9

A continuous change of a shape without cutting or joining parts

applies to shapes or functions more broadly, not limited to embeddings

Surface Forms

homotopy singular
homotopies plural

Morphology

homotopy = homo + topo + y

A technical mathematical term built from Greek combining forms ('homo-' + 'topo-') and a noun-forming suffix; its specialised meaning in topology is not derivable by an average B1 learner from the component pieces.

Etymology

The word homotopy comes from Greek parts homo- meaning 'same' and -topy (seen in topology) meaning 'place' or 'shape'. So a homotopy is a way to change or bend one shape into another while keeping them 'the same' in the important way, because you do it without cutting or gluing.