Thurston's jiggling

TL;DR

This paper offers a new, more conceptual proof of Thurston's jiggling lemma, extending its application to manifolds and clarifying the original technique introduced in the 1970s.

Contribution

It provides an alternative, more conceptual proof of Thurston's jiggling lemma and generalizes it to manifolds, which was previously only sketched.

Findings

New proof of Thurston's jiggling lemma

Generalization to manifolds proved

Clarifies the conceptual understanding of the technique

Abstract

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.