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.