Thurston's jiggling

In the 1970s Thurston introduced a technique known as ``jiggling'' which brings any triangulation into general position (a stronger version of transversality) by subdividing and perturbing. This result is now known as Thurston's jiggling lemma. In this paper we provide an alternative, more conceptual proof of the lemma. In particular we also prove the generalization to manifolds, whose proof had previously only been sketched.