homotopy
1
9.9
- noun
- /ˈhoʊməˌtoʊpi/
- Specialized
- His research focuses on homotopy theory, in particular the unstable homotopy theory of Lie groups and related objects.
Examples
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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.
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As for homotopy type theory, I don't know enough about that.
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posted by homotopy at 1:46 PM on March 6
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Posted by homotopy at 1:53 PM on March 6.
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In topology, a homotopy describes a continuous transformation from one geometric shape to another.
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Studying homotopy allows mathematicians to understand how different shapes can be related through continuous deformations.
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The concept of homotopy is essential in understanding the properties of spaces in algebraic topology.
Synonyms
A continuous change of a shape without cutting or joining parts
Surface Forms
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.