homotopy

(redirected from Homotopy equivalent)

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 ?
We should mention that Bjorner-Wachs and Randal-Williams actually proved the stronger result that |K(A)| is homotopy equivalent to a wedge of spheres of dimension |A| - 1.
For a finite geometric left regular band B, we will use the following special case of Rota's cross-cut theorem [26, 6] to provide a simplicial complex homotopy equivalent to the order complex [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] of B\{1}.
Keywords: Asymmetric reaction, nonhomogeneous differential opertator, C-condition, critical groups, homotopy equivalent, mountain pass theorem.
1 would therefore imply that, for such [sigma] and [tau], intervals [1, [tau]] and [[sigma], [tau]] are each either contractible or homotopy equivalent to a single sphere (of dimension [absolute value of [tau]] - 3 and [absolute value of [tau]] - [absolute value of [sigma]] - 2, respectively).
However, it is still open whether MacP(k, n) is homotopy equivalent to Gr(k, n).
A Stein manifold is homotopy equivalent to a finite dimensional CW-complex and when this complex is finite then [E.
0]) whose proper part is homotopy equivalent to [sub.
If G is finite then, rationally, it is homotopy equivalent to a product of Eilenberg-MacLane spaces as an H-space, implying that it is homotopy commutative.
The complex [DELTA] is called shellable if there exists a shelling order on its facets; it can be shown that any pure d-dimensional shellable simplicial complex is homotopy equivalent to a wedge of spheres, all of dimension d.
In fact, B C(E) is homotopy equivalent to a functor in the variable E [member of] [A.
Furthermore, the order complex of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is homotopy equivalent to a wedge of spheres of dimension k - 2.
The naive converse of this result is not true; namely there are spaces X and Y that are not homotopy equivalent but have isomorphic homotopy groups.