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 ?
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}.
Then K is homotopy equivalent to the order complex [DELTA](P).
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).
0]) whose proper part is homotopy equivalent to [sub.
0]) of a rank d arrangement A with base chamber c0 is homotopy equivalent to [S.
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.
Moreover, the complex [DELTA] is homotopy equivalent to a wedge of [h.
Furthermore, the order complex of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is homotopy equivalent to a wedge of spheres of dimension k - 2.
We now will use Quillen's fiber lemma to show that the chain complex [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is homotopy equivalent to the simplicial complex [[DELTA].
For a d-dimensional simplicial complex we have the following implications: shellable [right arrow] constructible [right arrow] homotopy Cohen-Macaulay [right arrow] homotopy equivalent to a wedge of d-dimensional spheres.
n]) \ {e} is homotopy equivalent to a wedge of (n - 2)-dimensional spheres and Cohen-Macaulay over Z.