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

Sullivan says that the result he is proudest of is one he obtained in 1977, which distils the crucial properties of a space using a tool called rational homotopy.

From Scientific American

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

From Scientific American

A homotopy equivalence is another type of continuous deformation, but in this case, you can identify distinct points.

From Scientific American

Another homotopy equivalence collapses the infinite expanse of three-dimensional Euclidean space down to a single point via a “reverse big bang” in which each point flies back to its origin, with the speed of this motion increasing with the distance from the location of the initial big bang.

From Scientific American