  The topology of $SU(3)$-representation varieties of the fundamental groups of
planar webs so that the meridians are sent to matrices with trace equal to $-1$
are explored, and compared to data coming from spider evaluation of the webs.
Corresponding to an evaluation of a web as a spider is a rooted tree. We
associate to each geodesic $\gamma$ from the root of the tree to the tip of a
leaf an irreducible component $C_{\gamma}$ of the representation variety of the
web, and a graded subalgebra $A_{\gamma}$ of $H^*(C_{\gamma};\mathbb{Q})$. The
spider evaluation of geodesic $\gamma$ is the symmetrized Poincare polynomial
of $A_{\gamma}$. The spider evaluation of the web is the sum of the symmetrized
Poincare polynomials of the graded subalgebras associated to all maximal
geodesics from the root of the tree to the leaves
