homotopy

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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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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}.
Keywords: Asymmetric reaction, nonhomogeneous differential opertator, C-condition, critical groups, homotopy equivalent, mountain pass theorem.
Hence by Lemma 5.7 we obtain a pointed G-action on a pointed space [Y.sub.*] homotopy equivalent to X.
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.sub.n](C(X)) = [bar.[E.sub.n](C(X))].
In this situation, we prove [bar.R](A, [r.sub.0]) is homotopy equivalent to a (rk A - 3)-sphere.
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.sub.p](G).
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.