  Topologically nontrivial fluctuations control the anomalous interactions for
the $\eta$ and and $\eta \prime$ pseudoscalar mesons. We consider the anomalous
interactions for mesons with higher spin, the heterochiral nonets with $J^{P C}
= 1^{+ -}$ and $2^{- +}$. Under the approximation of a dilute gas of
instantons, the mixing angle between non-strange and strange mesons decreases
strongly as $J$ increases, and oscillates in sign. Anomalous interactions also
open up new, rare decay channels. For glueballs, anomalous interactions
indicate that the $X(2600)$ state is primarily gluonic.
