homotopy

American  

[huh-mot-uh-pee, hoh-] / həˈmɒt ə pi, hoʊ- /

noun

Mathematics.

plural

homotopies

1. the relation that exists between two mappings in a topological space if one mapping can be deformed in a continuous way to make it coincide with the other.

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Etymology

Origin of homotopy

1915–20; homo- + -topy (< Greek tóp ( os ) place + -y ³, or < New Latin -topia )

Example Sentences

The researchers provide a unified skyrmion-hopfion homotopy classification and offer an insight into the diversity of topological solitons in three-dimensional chiral magnets.

From Science Daily • Nov. 22, 2023

This term refers to the notion of isomorphism in the more exotic homotopy category of spaces.

From Scientific American • Sep. 14, 2021

He added another invariant, known as the fundamental group, and believed that if a manifold had the same homotopy and fundamental group as a sphere, it had to be a sphere.

From Scientific American • Jun. 4, 2017

Motivic homotopy theory is blossoming, despite Voevodsky’s change of focus about ten years ago.

From Nature

In Voevodsky’s motivic homotopy theory, familiar classical geometry was replaced by homotopy theory — a branch of topology in which a line may shrink all the way down to a point.

From Nature