I will talk a method to construct normal subgroups isomorphic
to non-free right-angled Artin groups. This construction recovers,
expands, and makes constructive the result of Dahmani, Guirardel, and
Osin about free normal subgroups generated by a high power of a
pseudo-Anosov. We do this by creating a version of their “windmill”
construction tailor-made for the projection complexes introduced by
Bestvina, Bromberg, and Fujiwara. This is joint work with Johanna
Mangahas and Dan Margalit.