homotopy

(redirected from Homotopy class)

homotopy

[hō′mäd·ə·pē]
(mathematics)
Between two mappings of the same topological spaces, a continuous function representing how, in a step-by-step fashion, the image of one mapping can be continuously deformed onto the image of the other.
References in periodicals archive ?
It is usually formulated as finding navigation paths under homotopy class constraints.
The naive notion of a homotopy action of a group G on a topological space X can be described as the choice of a homotopy class of a map BG [right arrow] B haut(X), where haut(X) is the monoid of self-homotopy equivalences (see [section]1.
A homotopy action of G on X is therefore defined to be the homotopy class of a map [PHI] : BG [right arrow] B haut(X) (see [DDK, DW] and compare [Su]).
is (the homotopy class of) a map F* : BG [right arrow] B [haut.
0]) is (the homotopy class of) a map [PHI]* : BG [right arrow] [haut.
Thus the homotopy class of c is uniquely determined by the homotopy class of [bar.
Fix a homotopy class [f] [member of] [[summation]Y, BG].
When G = SU(3) then for any homotopy class [f] [member of] [[summation]Y, BSU(3)], Theorems 1.
Moreover, corresponding to each Y-cube there is a homotopy class [[alpha].