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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{massoni2026ziggurats,
  title = {{Ziggurats, taut foliations, and contact structures}},
  author = {Thomas Massoni and Jonathan Zung},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.30031},
  eprint = {2608.30031},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30031},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Ziggurats, taut foliations, and contact structures
AU  - Thomas Massoni
AU  - Jonathan Zung
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2608.30031
UR  - https://arxiv.org/abs/2608.30031
AB  - 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.
ER  -