  In models of composite Higgs dynamics new composite pseudoscalars can
interact with the Higgs and electroweak gauge bosons via anomalous
interactions, stemming from the topological sector of the underlying theory. We
show that a future 100 TeV proton-proton collider (FCC-pp) will be able to test
this important sector and thus shed light on the strong dynamics which
generates the Higgs and other composite states. To elucidate our results we
focus on the topological interactions of a minimal composite Higgs model with a
fermionic ultraviolet completion, based on the coset
$\text{SU}(4)/\text{Sp}(4)$. We suggest the strategy to test these interactions
at the FCC-pp and analyse the expected reach.
