  We use lattice topology as a laboratory to compare the Wilson action (WA)
with the Symanzik-Weisz (SW) action constructed from a combination of (1x1) and
(1x2) Wilson loops, and the estimate of the renormalization trajectory (RT)
from a renormalization group transformation (RGT) which also includes higher
representations of the (1x1) loop. Topological charges are computed using the
geometric (L\"uscher's) and plaquette methods on the uncooled lattice, and also
by using cooling to remove ultraviolet artifacts. We show that as the action
improves by approaching the RT, the topological charges for individual
configurations computed using these three methods become more highly
correlated, suggesting that artificial lattice renormalizations to the
topological susceptibility can be suppressed by improving the action.
