  One of the main open questions in liaison theory is whether every homogeneous
Cohen-Macaulay ideal in a polynomial ring is glicci, i.e. if it is in the
G-liaison class of a complete intersection. We give an affirmative answer to
this question for Stanley-Reisner ideals defined by simplicial complexes that
are weakly vertex-decomposable. This class of complexes includes matroid,
shifted and Gorenstein complexes respectively. Moreover, we construct a
simplicial complex which shows that the property of being glicci depends on the
characteristic of the base field. As an application of our methods we establish
new evidence for two conjectures of Stanley on partitionable complexes and on
Stanley decompositions.
