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

Vladimir Voevodsky revolutionized algebraic geometry and is best known for developing the new field of ‘motivic homotopy theory’.

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