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arXiv · 2608.30031

Ziggurats, taut foliations, and contact structures

Thomas Massoni·Jonathan Zung
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Abstract

We study the geography of taut foliations on compact $3$-manifolds with toroidal boundary components. The central object of our work is the set of boundary multislopes realized by foliations transverse to a fixed flow on such a manifold. We prove that these sets exhibit remarkable structural properties (rationality, rigidity, and convexity) which motivate the name ziggurats. Our main tool, of independent interest, is a two-way correspondence between foliations and contact structures on $3$-manifolds with boundary: we generalize the Eliashberg-Thurston theorem, which produces pairs of positive and negative contact structures from foliations, and a construction of the first author, which builds foliations from such contact pairs. Using both directions of this correspondence, we bring contact-geometric methods to bear on the architecture of ziggurats.

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Thomas Massoni, Jonathan Zung. 2026-09-02. Ziggurats, taut foliations, and contact structures. https://arxiv.org/abs/2608.30031

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