Geometric vertex decomposition and liaison are two frameworks that have been
used to produce similar results about similar families of algebraic varieties.
In this paper, we establish an explicit connection between these approaches. In
particular, we show that each geometrically vertex decomposable ideal is linked
by a sequence of elementary G-biliaisons of height 1 to an ideal of
indeterminates and, conversely, that every G-biliaison of a certain type gives
rise to a geometric vertex decomposition. As a consequence, we can immediately
conclude that several well-known families of ideals are glicci, including
Schubert determinantal ideals, defining ideals of varieties of complexes, and
defining ideals of graded lower bound cluster algebras.